![Page 1: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/1.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 2: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/2.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 3: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/3.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 4: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/4.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 5: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/5.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 6: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/6.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 7: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/7.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 8: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/8.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 9: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/9.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 10: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/10.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 11: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/11.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 12: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/12.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 13: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/13.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 14: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/14.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 15: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/15.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 16: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/16.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 17: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/17.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 18: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/18.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 19: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/19.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 20: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/20.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 21: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/21.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 22: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/22.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 23: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/23.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 24: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/24.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 25: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/25.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 26: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/26.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 27: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/27.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 28: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/28.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 29: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/29.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 30: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/30.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 31: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/31.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 32: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/32.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 33: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/33.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 34: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/34.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 35: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/35.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 36: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/36.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 37: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/37.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 38: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/38.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 39: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/39.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 40: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/40.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 41: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/41.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 42: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/42.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 43: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/43.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 44: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/44.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 45: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/45.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 46: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/46.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 47: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/47.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 48: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/48.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 49: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/49.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 50: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/50.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 51: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/51.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 52: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/52.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 53: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/53.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 54: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/54.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 55: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/55.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 56: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/56.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 57: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/57.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 58: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/58.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 59: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/59.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 60: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/60.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 61: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/61.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 62: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/62.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 63: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/63.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 64: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/64.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 65: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/65.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 66: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/66.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 67: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/67.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 68: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/68.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 69: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/69.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 70: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/70.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 71: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/71.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 72: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/72.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 73: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/73.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 74: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/74.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 75: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/75.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 76: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/76.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 77: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/77.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 78: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/78.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 79: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/79.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 80: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/80.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 81: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/81.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 82: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/82.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 83: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/83.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 84: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/84.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 85: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/85.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 86: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/86.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 87: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/87.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 88: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/88.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 89: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/89.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 90: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/90.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 91: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/91.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 92: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/92.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 93: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/93.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 94: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/94.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 95: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/95.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 96: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/96.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 97: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/97.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 98: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/98.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 99: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/99.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 100: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/100.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 101: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/101.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 102: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/102.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 103: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/103.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 104: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/104.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 105: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/105.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 106: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/106.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 107: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/107.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 108: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/108.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 109: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/109.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 110: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/110.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 111: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/111.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 112: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/112.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 113: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/113.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 114: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/114.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 115: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/115.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 116: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/116.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 117: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/117.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 118: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/118.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 119: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/119.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 120: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/120.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 121: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/121.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 122: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/122.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 123: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/123.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 124: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/124.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 125: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/125.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 126: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/126.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 127: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/127.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 128: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/128.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 129: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/129.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 130: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/130.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 131: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/131.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 132: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/132.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 133: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/133.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 134: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/134.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25
![Page 135: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/135.jpg)
©b B270X1T44 sKduxtSaI oSUoNfDt7wEaArjeQ dLtLZC5.6 3 pAxlWlu Lr0iugBhzthsz zrjeespearUvuerdK.I 9 sMEavdFev IwSiktVh5 UI7nafFiBnZiTt2eE 0AtlEgTerbxrvar I25.t Worksheet by Kuta Software LLC
Math Analysis Honors - Worksheet 96
©d H2j0Y1j45 MKRuNtnaZ SSWolfPtMwEaAroeF jLrLKCU.T S zA5ljlE irWiqgOhEtQsr 4rLeIsnevrCvqe1dc.H
Double-Angle and Half-Angle Identities
Use a double-angle or half-angle identity to find the exact value of each expression.
1) cos
7
π
82) sin
7
π
8
3) sin
165°4) sin
112
1
2°
5) sin
15°6) cos
23
π
12
7) sin
22
1
2° 8) sin
−5
π
12
9) cos
3
π
8
10) sin
75°
11) sin
θ =
−8
17 and 180° <
θ < 270°
Find cos
θ
2
12) sin
θ =
−7
25 and
3
π
2 <
θ < 2
π
Find sin
2
θ
13) sin
θ =
−9
22 and 270° <
θ < 360°
Find cos
2
θ
14) cos
θ =
4
5 and 270° <
θ < 360°
Find cos
θ
2
15) cos
θ =
−4
5 and −270° <
θ < −180°
Find sin
θ
2
16) cos
θ =
4
5 and 0 <
θ <
π
2
Find cos
2
θ
![Page 136: Double-Angle and Half-Angle Identities - sausd.us · ©f p2k0 T1m4A dKLunt na0 BS go 8fGt9w ra yr 3em JL dLNCW.1 4 ZAFlVlk Rrdi Oggh NtLsD 3rDe7s Ze br Sv deudz.l s GMCa1dje F vw](https://reader031.vdocument.in/reader031/viewer/2022021916/5e0bac5d6ff7d037880e5750/html5/thumbnails/136.jpg)
©f p2k0T1m4A dKLuntna0 BSgo8fGt9wrayr3em JLdLNCW.1 4 ZAFlVlk RrdiOgghNtLsD 3rDe7sZebrSvdeudz.l s GMCa1djeF vwNiYtmhD BIpn9f3iRn2i7tReC kA8lRgQe3byrwa1 l2r.l Worksheet by Kuta Software LLC
Answers to Double-Angle and Half-Angle Identities
1)
−
2 + 2
22)
2 −
2
2
3)
6 −
2
44)
2 + 2
2
5)
6 −
2
46)
6 + 2
47)
2 −
2
2
8)
− 6 −
2
4
9)
2 −
2
2
10)
6 + 2
411)
−
17
17
12)
−336
625
13)
161
24214)
−
3 10
1015)
−
3 10
10
16)
7
25