Download Right Triangle Trigonometry

Right Triangle
Trigonometry
Objectives:
Evaluate trigonometric functions of acute angles
Use the fundamental trigonometric identities
Use trigonometric functions to model and solve real-life problems
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4.3 Right Triangle Trigonometry
Precalculus
adj

Precalculus
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4.3 Right Triangle Trigonometry
Trigonometric Functions
hyp
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4.3 Right Triangle Trigonometry
Precalculus
Example 1
• cos  =
• tan  =
• csc  =
5 
13
12
• sec  =
Precalculus
• sin  =
4.3 Right Triangle Trigonometry
• Evaluate the six trig
functions of the angle
 shown in the right
triangle
• cot  =
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YOU TRY
• cos  =
• tan  =
• csc  =
• sec  =
Precalculus
• sin  =
4.3 Right Triangle Trigonometry
• Evaluate the six trig
functions of the angle
 shown in the right
triangle
• cot  =
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4.3 Right Triangle Trigonometry
Precalculus
Example 2
Find cos 𝜃 if tan 𝜃 = .
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4
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Precalculus
Find sec 𝜃 if sin 𝜃 =
4.3 Right Triangle Trigonometry
You Try
3
.
2
8
• sin
𝜋
6
• cos 120°
• tan 45°
csc 63°
2𝜋
sec
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4.3 Right Triangle Trigonometry
• Evaluating the following to the nearest hundredths using a
calculator:
Precalculus
Example 3
cot 250°
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Example 4
30°
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4.3 Right Triangle Trigonometry
Precalculus
• Find the value of x for the right triangle shown
x
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c
A
b
B
62°
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C
4.3 Right Triangle Trigonometry
• Solve ∆ABC (i.e. find the measures of all the unknown angles
and sides of the triangle).
Precalculus
Example 5
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B
c
A

30°
a
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C
4.3 Right Triangle Trigonometry
Precalculus
You Try
• Solve ∆ABC.
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B
15
A
9
C
4.3 Right Triangle Trigonometry
• Find the measure of angle B to the nearest tenth (ONE
decimal place ).
• .
Precalculus
Example 6
13
B
12
A
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C
4.3 Right Triangle Trigonometry
Find the measure of angle A to the nearest hundredths (TWO
decimal places ).
Precalculus
You Try
14
B
c
A
5
9
C
4.3 Right Triangle Trigonometry
• Solve ∆ABC (i.e. find the measures of all the unknown angles
and sides of the triangle).
Precalculus
Example 7
15
B
12
A
2
C
4.3 Right Triangle Trigonometry
Precalculus
You Try
• Solve ∆ABC.
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
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4.3 Right Triangle Trigonometry
Precalculus
4.3 Right Triangle Trigonometry
Precalculus
Victory Lap
Find the unknown value:
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