Download Right Triangle Trigonometry - Social Circle City Schools

Bellwork
Rationalize the denominators
· 1
2
·
1
3
·
2
3
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
Precalculus
4.3 Right Triangle Trigonometry
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4.3 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
Trigonometric Functions
Given a right triangle with acute angle 


Precalculus
opp
sin  
hyp
hyp
csc  
opp
adj
cos  
hyp
hyp
sec  
adj
opp
tan  
adj


adj
cot  
opp
4.3 Right Triangle Trigonometry
opp
hyp
adj

3
Example 1
· Evaluate the six trig
functions of the
angle  shown in the
right triangle
· sin  =
5 
· csc  =
13
· cos  =
· tan  =
· sec  =
12
· cot  =
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4.3 Right Triangle Trigonometry
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Example 2
· Find the value of x for the right triangle
shown
30°
15
x
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Example 3
· Solve ∆ABC
c
A
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b
B
62°
6
C
4.3 Right Triangle Trigonometry
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You Try
· Solve ∆ABC
B
c
A

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30°
a
15
C
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Special Triangles
30º-60°-90°
60°
1
Recall the conversions
2

60°= 3

30°= 6
30°
3

1
sin 30  sin 
6 2



3
3 2

3

 1
cos30  cos 
cos60  cos 
2
6
3 2
 



1
3
3
tan 30  tan 
tan60  tan 

 3
6
3 1
3
3
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4.3 Right

Triangle Trigonometry 
sin 60  sin

8
Special Triangles
45º-45°-90°
Recall the conversion
45°

45°= 4
2
1
45°

1

sin 45  sin

4

1
2

2
2

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1
2
cos45  cos 

4
2
2


 1
tan 45  tan   1
4 1
4.3 Right Triangle Trigonometry
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Co-functions of
Complementary Angles
· Look back at the sines and cosines for
the 30-60-90 triangle
· Note that sin 30°=cos 60°
· Co-functions of complementary angles
are equivalent
Precalculus
sin 90    cos
cos90    sin 
tan90    cot 
cot 90    tan 
sec90    csc 
csc90    sec 
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Trigonometric Identities
· Reciprocal Identities



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1
sin  
csc 
1
csc  
sin 
1
cos 
sec 
1
sec  
cos
1
tan  
cot 


1
cot  
tan 
4.3 Right Triangle Trigonometry

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You Try: Classwork
· Label Assignment: CW 4.3
· Pg. 310: #5, 7, 11
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Trigonometric Identities
· Quotient Identities
sin 
tan  
cos

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cos
cot  
sin 

4.3 Right Triangle Trigonometry
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Trigonometric Identities
· Pythagorean Identities
sin 2   cos 2   1
1 tan 2   sec 2 



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1 cot 2   csc 2 
Note: sin2 is (sin )2 not sin (2)
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Example 4
· Given sin=0.6, find the value of cos
· Given sin=0.6, find the value of tan
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Example 5
Use trigonometric identities to transform
one side of the equation into the other.
· cossec=1
· (sec+tan)(sec-tan)=1
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Example 6
· You are standing 75 meters from the base of
the Jin Mao Building in Shanghai, China. You
estimate that the angle of elevation to the top of
the building is 80°.
· What is the approximate height of the
building?
· Suppose one of your friends is at the top of the
building. What is the distance between you and
your friend?
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4.3 Right Triangle Trigonometry
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Closure
· What is the relationship of the sine to the
cosecant?
· What is the relationship of the sine to the
cosine?
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You Try: Classwork
· Label Assignment: CW 4.3
· Pg. 310: #19, 23, 25-39 odd, 43-63 odd
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Homework
· Label Assignment: HW 4.3
· Pg. 310: #4, 8, 14, 20, 22, 26-38 even,
44-62 even, 70, 74, 76, 78
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