2.2 trigonometric functions of special angles obj: find 6 trigonometric functions of the special...
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2.2 Trigonometric Functions Of Special Angles
OBJ: Find 6 trigonometric functions of the special angles
Evaluate trigonometric expressions
Special Angles
Trigonometric Functions
DEF: 30-60-90 60º
30º SOH CAH TOA
Sin Oh__
___ Heck
Cos Another
= Hour
Tan Of___
Algebra
Sin Opp
Hyp
Csc Hyp
Opp
Cos Adj
Hyp
Sec Hyp
Adj
Tan Opp
Adj
Cot Adj
Opp
2 1
3
DEF: 30-60-90 2 60º 1
30º √3SOH CAH TOA
Sin Oh__
___ Heck
Cos Another
= Hour
Tan Of___
Algebra
Sin Opp
Hyp
Csc Hyp
Opp
Cos Adj
Hyp
Sec Hyp
Adj
Tan Opp
Adj
Cot Adj
Opp
EX: Find the trigonometric function values for 30°
2 60º
1
30º √3
Sin
Csc
Cos Sec
Tan Cot
EX: Find the trigonometric function values for 30°
2 60º
1
30º √3
Sin
1
2 Csc
2
Cos
√ 3
2 Sec
2√ 3
3
Tan
√ 3
3 Cot
√ 3
2 1
3
EX: Find the trigonometricfunction values for 210
Sin Csc
Cos Sec
Tan Cot
-√ 3
-1
2
y
x
5
5
-5-5
EX: Find the trigonometricfunction values for 210
Sin
-1
2
Csc -2
Cos -√ 3
2
Sec -2√ 3
3
Tan
√ 3
3
Cot √ 3
-√ 3
-1
2
y
x
5
5
-5-5
DEF: 45-45-90
Sin Csc
Cos Sec
Tan Cot
2 1
1
DEF: 45-45-90
Sin Csc
Cos Sec
Tan Cot
√2 1
1
DEF: 45-45-90
Sin √2
2
Csc √2
Cos √2
2
Sec √2
Tan 1 Cot 1
√2 1
1
2 1
1
EX: Find the trigonometricfunction values for 315
Sin Csc
Cos
Sec
Tan Cot
1
√2-1
y
x
5
5
-5-5
EX: Find the trigonometricfunction values for 315
Sin -√2
2
Csc -√2
Cos
√2
2
Sec √2
Tan -1 Cot -1
y
x
5
5
-5-5
1
√2 -1
2 3
1
EX: Find the trigonometric 30º function values for 60° 2 √3
60º1
Sin Csc
Cos Sec
Tan Cot
EX: Find the trigonometric 30º function values for 60° 2 √3
60º1
Sin
√ 3
2 Csc
2√ 3
3
Cos
1
2 Sec
2
Tan
√ 3
Cot
√ 3
3
2 3
1
EX: Find the trigonometric function values for
Sin 30 = Cos 60
Sin
1
2 Csc
2
Cos
√ 3
2 Sec
2√ 3
3
Tan
√ 3
3 Cot
√ 3
Sin
√ 3
2 Csc
2√ 3
3
Cos
1
2 Sec
2
Tan
√ 3
Cot
√ 3
3
EX: Evaluate cos60+2sin260–tan230
½ + 2(√3/2 )2 – (1/√3)2
½ + 2(¾) – ⅓
½ + 3/2 – ⅓
2 – ⅓
5/3 or 1 ⅔
Evaluate each of the following:29) sin 2 120 + cos 2 120(√3/2 )2 + (-½)2
¾ + ¼
1
(Pythagorean) Identity
sin 2 + cos 2 = 1
31)2tan2120 + 3sin2150 – cos2180
2(-√3)2 + 3(½)2 – (-1)2
2(3) + 3( ¼) – 1
5 ¾
33) sin 2 225 – cos 2 270 + tan 60
(-1/√2)2 – (0)2 + √3
½ + √3
35)cos2 60 + sec 2 150 – csc 2 210
(½)2 + (-2/√3)2 – (-2)2
¼ + 4/3 – 4
3/12 + 16/12 – 48/12
- 27/12
- 9/4
37) sec 30 – sin 60 + cos 210
2√3 – √3 – √3
3 2 2
4√3 – 3√3 – 3√3
6 6 6
-2 √3 = -√3
6 3
True or False39)sin 30 + sin 60 = sin ( 30 + 60 )½ + √3/2 1
False
41) cos 60 = 2 cos 2 30 – 1
½ 2 (√3/2)2 – 1
2 (¾) – 1
3/2 – 1
½
True
43) sin 120 = sin 150 – sin 30
√3/2 ½ – ½
0
False
45)sin120=sin180cos60–sin60cos180
√3/2 (0)(½) – (√3/2)(-1)
True
Identity
sin (1 – 2)
sin(180 – 60) = sin180cos60–sin60cos180
47)cos150=cos120cos30–sin120sin 30
-√3/2 (-½)(√3/2) – (√3/2)(½)
-√3/4 – √3/4
-√3/2
True
Identity
cos (1 + 2)
cos(120 + 30)=cos120cos30–sin120sin 30