find the missing measures. write all answers in radical form
DESCRIPTION
Find the missing measures. Write all answers in radical form. 30 °. 45 °. x. 7. 10. z. 45 °. w. 60 °. y. The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions. SIN E. COS INE. TAN GENT. SIN E. Prounounced “sign”. COS INE. - PowerPoint PPT PresentationTRANSCRIPT
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Find the missing measures. Write all answers in radical form.
45°
45° x
w
7
60°
30°
10
y
z
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The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
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The Trigonometric Functions
SINE
COSINE
TANGENT
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SINE
Prounounced “sign”
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Prounounced “co-sign”
COSINE
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Prounounced “tan-gent”
TANGENT
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Prounounced “theta”
Greek Letter
Represents an unknown angle
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oppositehypotenuse
OppSin
Hyp
adjacent
AdjCos
Hyp
OppTan
Adj
hypotenuseopposite
adjacent
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We need a way to remember all of these ratios…
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Old Hippie
Old Hippie
SomeOldHippieCameAHoppin’ThroughOurApartment
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SOHCAHTOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
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Finding sin, cos, and tan
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6
8
10
SOHCAHTOA
10
8
10
6
6
8
OppSin
Hyp
CosAdj
Hyp
TanOpp
Adj
4
5
3
5
4
3
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Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
hypo
oppAsin
8.10
9 8333.
hypo
adjAcos
8.10
6 5555.
adj
oppAtan
6
9 5.1
9
6
10.8
A
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Find the values of the three trigonometric functions of .
4
3
? Pythagorean Theorem:(3)² + (4)² = c²
5 = c
opp
hyp 4
5
adj
hyp
3
5 opp
adj
4
3
sin cos tan
5
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Find the sine, the cosine, and the tangent of angle A
A
24.5
23.1
8.2
hypo
oppAsin
5.24
2.8 3347.
hypo
adjAcos
5.24
1.23 9429.
adj
oppAtan
1.23
2.8 3550.
B Give a fraction and decimal answer (round to 4 decimal places).
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Let’s find the calculator connections.
Draw a 30º-60º-90º to help you find sin 30º.
Now use your calculator to find sin 30º.
So… What is sin 45º?
What is cos 27º?
What is tan 62º?
1
.8910
1.881
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Can using the calculator help us solve this problem?
In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides.
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Can using the calculator help us solve this problem?
In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides.
Q
16
P R
35PR
tan3516
16 tan35 PR
PR 11.20
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Can using the calculator help us solve this problem?
In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides.
Q
16
P R
35
16cos35
QR
QR cos35 16
16QR
cos35QR 19.53
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What about indirect measurement?
• The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding
the kite to the ground,
how high is the kite
actually flying?
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Solution:
• The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite
to the ground, how high is the kite flying?
100’
79º
hsin79
100100 sin79 h
98.16'
h
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A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?
50
71.5°
x
tan 71.5°
tan 71.5°50
x
x = 50 (tan 71.5°)
x = 50 (2.98868)
149.4x ft
You try….
Opp
Hyp
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A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge?
200
x
60°
cos 60°
x (cos 60°) = 200
x
X = 400 yards