1. Identities: Pythagorean and Sum and Difference
Section 7.1
Identities: Pythagorean and Sum and Difference
Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

2. Objectives State the Pythagorean identities.
Simplify and manipulate expressions containing trigonometric expressions.
Use the sum and difference identities to find function values.

3. Basic Identities

4. Pythagorean Identities
Recall the equation of a unit circle in the xy-plane

5. Pythagorean Identities
We can develop two other Pythagorean identities.

6. Pythagorean Identities
Equivalent Forms
Pythagorean Identities

7. Example
Factor and simplify
Solution:

8. Example Simplify each of the following trigonometric expressions.
Solution:

9. Example (cont)

10. Example
Add and simplify
Solution:

11. Example
Express as a trigonometric function of  without using radicals by letting x = 3 tan Assume that 0 <  < π/2. Then find sin  and cos .
Solution:

12. Example (cont)

13. Sum and Difference Identities

14. Example
Find cos (5π/12) exactly.
Solution:

15. Example
Find tan 15 exactly.
Solution: