Section 6.2
Trigonometric Functions:
Unit Circle Approach
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
 2 2
,


2
2


Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Make a second congruent triangle.
This triangle is equilateral so all
1
sides are 1. 2a = 1 so a = 2 .
Use Pythagorean Theorem to
find b.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the exact value of each expression.
(a) cos135
(b) tan
3
4
(c) sin 225
 5 
(d) cos  

 4 

2 2
2
(a) The point  
,
corresponds
to
35

so
cos
135




2
2
2



2 2
3
(b) The point  
,
 corresponds to
4
 2 2 
2
3
so tan
 2  1
4
2

2
(e) sin
9
4
Find the exact value of each expression.
(a) cos135
(b) tan
3
4
(c) sin 225
 5 
(d) cos  

 4 
(e) sin

2
2
2
(c) The point  
,
corresponds
to
225

so
sin
225




2
2
2



2 2
5
 5
(d) The point  
,
corresponds
to

so
cos


4
 4
 2 2 
 2 2
9
(e) The point 
,
corresponds
to

2
2
4


9
2
so sin

4
2
2




2

9
4
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find: (a) cos 150
(b) sin (  30)
5
3
(a) cos 150  cos

6
2
1
 
(b) sin (  30)  sin     
2
 6
 7 
(d) sin 

 6 
3

4
(c) tan
 2  3
1
3

2
1
 7 
(d) sin 



2
 6 
(c) tan
4
3
Your calculator has buttons for sin, cos, and tan so to find
values of the remaining 3 trigonometric functions we use:
CHANGE MODE
TO RADIANS
a  4 and b  3 so r  a2  b2  16  9  5