1. Multiple-Angle and Product-Sum Formulas
Section 5.5
Multiple-Angle and Product-Sum Formulas

2. Objective By following instructions students will be able to:
Use multiple-angle formulas to rewrite and evaluate trigonometric functions.
Use power-reducing formulas to rewrite and evaluate trigonometric functions.
Use half-angle formulas to rewrite and evaluate trigonometric functions.
Use product-sum formulas to rewrite and evaluate trigonometric functions

3. Double-Angle Formulas
Note:

4. Example 1: Solving a Multiple-Angle Equation
Find all solutions of

5. Example 2: Using Double-Angle Formulas in Sketching Graphs
Analyze the graph of over the interval

6. Example 3: Evaluating Functions Involving Double Angles
Use the following to find , , and . , where

7. Example 4: Deriving a Triple-Angle Formula
Express in terms of

8. Power-Reducing Formulas

9. Example 5: Reducing a Power
Rewrite as a sum of first powers of the cosines of multiple angles.

10. Half-Angle Formulas
Note: The signs of sin(u/2) and cos(u/2) depend on the quadrant u/2 lies.

11. Example 6: Using a Half-Angle Formula
Find the exact value of

12. Example 7: Solving a Trigonometric Function
Find all solutions of in the interval .

13. Product-to-Sum Formulas

14. Example 8: Writing Products as Sums
Rewrite the product as a sum or difference.

15. Sum-to-Product Formulas

16. Example 9: Using a Sum-to-Product Formula
Find the exact value of

17. Example 10: Solving a Trigonometric Equation
Find all solutions of in the interval .

18. Example 11: Verifying a Trigonometric Identity
Verify the identity

19. Revisit Objective Did we…
Use multiple-angle formulas to rewrite and evaluate trigonometric functions?
Use power-reducing formulas to rewrite and evaluate trigonometric functions?
Use half-angle formulas to rewrite and evaluate trigonometric functions?
Use product-sum formulas to rewrite and evaluate trigonometric functions?

20. Homework
Pg 418 #1-79 EOO