Transcript 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
2
4.3 Right Triangle Trigonometry
Precalculus
adj

Precalculus
opp
4.3 Right Triangle Trigonometry
Trigonometric Functions
hyp
3
4
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  =
5
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  =
6
4.3 Right Triangle Trigonometry
Precalculus
Example 2
Find cos 𝜃 if tan 𝜃 = .
1
4
7
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
3
4.3 Right Triangle Trigonometry
• Evaluating the following to the nearest hundredths using a
calculator:
Precalculus
Example 3
cot 250°
9
Example 4
30°
15
4.3 Right Triangle Trigonometry
Precalculus
• Find the value of x for the right triangle shown
x
10
c
A
b
B
62°
6
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
11
B
c
A

30°
a
15
C
4.3 Right Triangle Trigonometry
Precalculus
You Try
• Solve ∆ABC.
12
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
15
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.
16
17
4.3 Right Triangle Trigonometry
Precalculus
18
4.3 Right Triangle Trigonometry
Precalculus
19
4.3 Right Triangle Trigonometry
Precalculus
20
4.3 Right Triangle Trigonometry
Precalculus
21
4.3 Right Triangle Trigonometry
Precalculus
22
4.3 Right Triangle Trigonometry
Precalculus
23
4.3 Right Triangle Trigonometry
Precalculus
24
4.3 Right Triangle Trigonometry
Precalculus
25
4.3 Right Triangle Trigonometry
Precalculus
26
4.3 Right Triangle Trigonometry
Precalculus
4.3 Right Triangle Trigonometry
Precalculus
Victory Lap
Find the unknown value:
27