1. Copyright © 2011 Pearson, Inc.

2. 5.1 Fundamental Identities Goal: Use the fundamental identities to simplify trigonometric expressions.

3. Copyright © 2011 Pearson, Inc. Slide 5.1 - 3 What you’ll learn about Identities Basic Trigonometric Identities Pythagorean Identities Cofunction Identities Odd-Even Identities Simplifying Trigonometric Expressions Solving Trigonometric Equations … and why Identities are important when working with trigonometric functions in calculus.

4. Copyright © 2011 Pearson, Inc. FYI

5. Copyright © 2011 Pearson, Inc. Slide 5.1 - 5 Basic Trigonometric Identities

6. Copyright © 2011 Pearson, Inc. Slide 5.1 - 6 Pythagorean Identities

7. Copyright © 2011 Pearson, Inc. Slide 5.1 - 7 Cofunction Identities

8. Copyright © 2011 Pearson, Inc. Slide 5.1 - 8 Even-Odd Identities

9. Copyright © 2011 Pearson, Inc. Simplification Ideas  Rewrite tan, cot, sec, and csc in terms of sin and cos.  Expand Products  Example: (1 + sin x)(1 – sin x) = 1 – sin x + sin x – sin 2 x  Factor  Example: sinxcosx – sinx = sinx(cosx – 1)  Take Square Roots  Combining Fractions

10. Copyright © 2011 Pearson, Inc. Slide 5.1 - 10 Simplify by Rewriting

11. Copyright © 2011 Pearson, Inc. Slide 5.1 - 11 Simplify by Expanding Products

12. Copyright © 2011 Pearson, Inc. Slide 5.1 - 12 Simplifying by Factoring

13. Copyright © 2011 Pearson, Inc. Slide 5.1 - 13 Simplify by Taking Square Roots

14. Copyright © 2011 Pearson, Inc. Slide 5.1 - 14 Simplify by Combining Fractions

15. Copyright © 2011 Pearson, Inc. Slide 5.1 - 15 Example Simplifying by Expanding and Using Identities

16. Copyright © 2011 Pearson, Inc. 5.1 Day 2 Fundamental Identities Goal: Solve trigonometric equations.

17. Copyright © 2011 Pearson, Inc. Warm Up Slide 5.1 - 17

18. Copyright © 2011 Pearson, Inc. Example 1: Using the Pythagorean Identity Slide 5.1 - 18

19. Copyright © 2011 Pearson, Inc. Example 2a: Solving Trigonometric Equations by Factoring Slide 5.1 - 19

20. Copyright © 2011 Pearson, Inc. Example 2b: Solving Trigonometric Equations by Factoring Slide 5.1 - 20

21. Copyright © 2011 Pearson, Inc. Example 2c: Solving Trigonometric Equations by Factoring Slide 5.1 - 21