1. Using Fundamental Identities
Skill 31

2. Objectives…
Recognize and write the fundamental trigonometric identities.
Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions.
Verify trigonometric identities.

3. Introduction
Here, we will learn how to use the fundamental identities to do the following.
1. Evaluate trigonometric functions.
2. Simplify trigonometric expressions.
3. Develop additional trigonometric identities.
4. Solve trigonometric equations.

6. Using the Fundamental Identities
One common use of trigonometric identities is to use given values of trigonometric functions to evaluate other trigonometric functions.

7. Example–Using Identities to Evaluate a Function
sec u = and tan u > 0
Find the values of all six trigonometric functions.
Solution:
sin2 u = 1 – cos2 u
Because sec u < 0 and tan u > 0,
it follows that u lies in Quadrant III.

8. Example–Solution

9. Example–Simplifying Trigonometric Expressions

10. Example–Simplifying Trigonometric Expressions

11. Example–Simplifying Trigonometric Expressions

12. 31 Using Fundamental Identities
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