Section 6.2 trigonometric functions unit circle approach

Section 6.2

Trigonometric Functions:

Unit Circle Approach

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.








2 2,2 2



Make a second congruent triangle.

Use Pythagorean Theorem to find b.

This triangle is equilateral so all sides are 1. 2a = 1 so a = .

12




Find the exact value of each expression.3 5 9(a) cos135 (b) tan (c) sin 225 (d) cos (e) sin4 4 4

2 2 2(a) The point , corresponds to 35 so cos 1352 2 2

2 2 3(b) The point , corresponds to 2 2 4

23 2so tan 14 2

2

Find the exact value of each expression.3 5 9(a) cos135 (b) tan (c) sin 225 (d) cos (e) sin4 4 4

2 2 2(c) The point , corresponds to 225 so sin 2252 2 2

2 2 5 5 2(d) The point , corresponds to so cos2 2 4 4 2

2 2 9(e) The point , corresponds to 2 2 4

9 2so sin4 2


4 7Find: (a) cos 150 (b) sin ( 30 ) (c) tan (d) sin3 6

5 3(a) cos 150 cos6 2

1(b) sin ( 30 ) sin6 2

34 2(c) tan 313

2

7 1(d) sin6 2

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

2 24 and 3 so 16 9 5a b r a b