13.1 – Use Trig with Right Triangles
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Transcript of 13.1 – Use Trig with Right Triangles
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13.1 – Use Trig with Right Triangles
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Hypotenuse:
Opposite side:
Adjacent side:
Side opposite right angle
Hypotenuse
Side opposite reference angle
Op
pos
ite
Side next to reference angle, not hypotenuse
Adjacent
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HypotenuseOp
pos
ite
Adjacent
sin = opphyp
cos = adjhyp
tan = oppadj
csc = hypopp
sec = hypadj
cot = adjopp
csc = 1 .
sin sec = 1 .
cos cot = 1 .
tan
csc = cosecant
sec = secant
cot = cotangent
SOH – CAH – TOA
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1. Evaluate the six trigonometric functions of the angle .
sin = 915
cos = 1215
tan = 912
csc = 15 9
sec = 1512
cot = 12 9
c2 = a2 + b2
152 = a2 + 92
225 = a2 + 81144 = a2
12 = a12
H
A
O
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2. Let be an acute angle of a right triangle. Find the value of the other five trigonometric functions of .
4sin
5
4 5
c2 = a2 + b2
52 = a2 + 42
25 = a2 + 169 = a2
3 = a
sin = 45
cos = 35
tan = 43
csc = 54
sec = 53
cot = 34
3
H
A
O
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2. Let be an acute angle of a right triangle. Find the value of the other five trigonometric functions of .
21
c2 = a2 + b2
c2 = 1 + 3c2 = 4c = 2
sin = 45
cos = 35
tan = 43
csc = 54
sec = 53
cot = 34
cot 3
3
cot = adjopp
22 21 3c H
A
O
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3. Find the measure of the missing sides. Round to the nearest hundredth.
c dH
A
Osin 42° =
c7
7 sin 42° = c
1
4.68 = c
cos 42° =d7
7 cos 42° = d
1
5.20 = d
SOH – CAH – TOA
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3. Find the measure of the missing sides. Round to the nearest hundredth.
a b
tan 57° = 14 a
a tan 57° = 14
1
a = 9.09
sin 57° = 14 b
b sin 57° = 14
1
16.69 = b
H
O
A
SOH – CAH – TOA
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4. Solve ABC, using the diagram and the given measurements.
A = 40°, c = 8 A
B
C
a
b
c
40° 8H
O
A 50°
40°
90°
8
a b
sin 40° = a8
8 sin 40° = a
1
a = 5.14
cos 40° = b8
8 cos 40° = b
1
6.13 = b
SOH – CAH – TOA
5.14
6.13
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Remember special triangles?
45° 45° 90°
1 1 2
1
1
2
30° 60° 90°
1 23
21
345°
45° 60°
30°
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5. Find the exact values of the variables.
1
1
2 x = 13
y = 13 2
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5. Find the exact values of the variables.
x =
14y =
7 3
2
13
60°
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2
1
3
5. Find the exact values of the variables.
x = 3
y = 3 3
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5. Find the exact values of the variables.
2
1
3
x = 18
3
3
3
18 3
36 3
y = 12 3