Section 6.2 trigonometric functions unit circle approach

1. Section 6.2
Trigonometric Functions:
Unit Circle Approach

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18. 2 2
,
2 2
 
 ÷ ÷
 

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Make a second congruent triangle.
Use Pythagorean Theorem to
find b.
This triangle is equilateral so
all sides are 1. 2a = 1 so a = .
1
2

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27. Find the exact value of each expression.
3 5 9
(a) cos135 (b) tan (c) sin 225 (d) cos (e) sin
4 4 4
π π π 
° ° − ÷
 
2 2 2
(a) The point , corresponds to 35 so cos 135
2 2 2
 
− ° ° = − ÷ ÷
 
2 2 3
(b) The point , corresponds to
2 2 4
2
3 2so tan 1
4 2
2
π
π
 
− ÷ ÷
 
= = −
−

28. Find the exact value of each expression.
3 5 9
(a) cos135 (b) tan (c) sin 225 (d) cos (e) sin
4 4 4
π π π 
° ° − ÷
 
2 2 2
(c) The point , corresponds to 225 so sin 225
2 2 2
 
− − ° ° = − ÷ ÷
 
2 2 5 5 2
(d) The point , corresponds to so cos
2 2 4 4 2
π π   
− − − = − ÷  ÷ ÷   
2 2 9
(e) The point , corresponds to
2 2 4
9 2
so sin
4 2
π
π
 
 ÷ ÷
 
=

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30. 4 7
Find: (a) cos 150 (b) sin ( 30 ) (c) tan (d) sin
3 6
π π 
° − °  ÷
 
5 3
(a) cos 150 cos
6 2
π
° = = −
1
(b) sin ( 30 ) sin
6 2
π 
− ° = − = − ÷
 
3
4 2(c) tan 3
13
2
π −
= =
−
7 1
(d) sin
6 2
π 
= − ÷
 

32. Your calculator has buttons for sin, cos, and tan so to find
values of the remaining 3 trigonometric functions we use:

36. 2 2
4 and 3 so 16 9 5a b r a b= = − = + = + =