2. Copyright © 2011 Pearson, Inc. Warm Up What is the Pythagorean Identity?

3. Copyright © 2011 Pearson, Inc. 5.4 Multiple Angle Identities Goal: Apply the double-angle identities.

4. Copyright © 2011 Pearson, Inc. Slide 5.4 - 3 What you’ll learn about Double-Angle Identities Power-Reducing Identities Half-Angle Identities Solving Trigonometric Equations … and why These identities are useful in calculus courses.

5. Copyright © 2011 Pearson, Inc. Slide 5.4 - 4 Double Angle Identities

6. Copyright © 2011 Pearson, Inc. Proving a Double-Angle Identity Prove. Slide 5.4 - 5

7. Copyright © 2011 Pearson, Inc. Proving a Double-Angle Identity Slide 5.4 - 6

8. Copyright © 2011 Pearson, Inc. When α = 30°, verify the identity for sin 2α.

9. Copyright © 2011 Pearson, Inc. #1 Rewrite in a simpler form.

10. Copyright © 2011 Pearson, Inc. #2 Rewrite in a simpler form.

11. Copyright © 2011 Pearson, Inc. #3 Rewrite in a simpler form.

12. Copyright © 2011 Pearson, Inc. #4 Rewrite in a simpler form.

13. Copyright © 2011 Pearson, Inc. #5 Rewrite in a simpler form.

14. Copyright © 2011 Pearson, Inc. #6 Rewrite in a simpler form.

15. Copyright © 2011 Pearson, Inc. #7 Evaluate without a calculator.

16. Copyright © 2011 Pearson, Inc. #8 Evaluate without a calculator.

17. Copyright © 2011 Pearson, Inc. Slide 5.4 - 16 Half-Angle Identities