1. Multiple-Angle and Product-to-Sum Formulas (Section 5-5)

2. Double-Angle Formulas

3. Example 1 Use the figure to find the exact value.
sin x
cos x
cos 2x
sin 2x
tan 2x
sec 2x
csc 2x
cot 2x 8 15 17

4. Find the exact solutions of the equation algebraically on the interval [0, 2π).
Example 2

5. Find the exact solutions of the equation algebraically on the interval [0, 2π).
Example 3

6. Find the exact solutions of the equation algebraically on the interval [0, 2π).
Example 4

7. Find the exact solutions values of sin 2u, cos 2u, and tan 2u using the double-angle formulas.
Example 5

8. Find the exact solutions values of sin 2u, cos 2u, and tan 2u using the double-angle formulas.
Example 6

9. Use a double angle formula to rewrite the expression.
Example 7

10. Use a double angle formula to rewrite the expression.
Example 8

11. Power Reducing Formulas

12. Rewrite the expression in terms of the first power of cosine.
Example 9

13. Rewrite the expression in terms of the first power of cosine.
Example 10

14. HW #23 pg 394 (1-35odd)

15. Half-Angle Formulas

16. Example 11 Use the figure to find the exact value of each trigonometric function.3 4 5 θ a) b) c) d) e) f)

17. Example 12 Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.

18. Example 13 Find the exact values of the sin (u/2), cos(u/2), and tan(u/2) using the half-angle formulas.

19. Example 14 Use the half-angle formulas to simplify the expression.

20. Example 15 Find the solutions of the equation in the interval [0, 2π).

21. HW #24 pg 395 (37-59odd)

22. Product-to-Sum Formulas

23. Use the product-to-sum formulas to write the product as a sum or difference.
Example 16

24. Use the product-to-sum formulas to write the product as a sum or difference.
Example 17

25. Use the product-to-sum formulas to write the product as a sum or difference.
Example 18

26. Sum-to-Product Formulas

27. Use the sum-to-product formulas to write the sum or difference as a product.
Example 19

28. Use the sum-to-product formulas to write the sum or difference as a product.
Example 20

29. Use the sum-to-product formulas to find the exact value of the expression.
Example 21

30. Find the solutions of the equation in the interval [0, 2π)
Example 22

31. HW #25 pg (61-87odd)

32. Verify the identity algebraically.
Example 23

33. Verify the identity algebraically.
Example 24

34. Verify the identity algebraically.
Example 25

35. Verify the identity algebraically.
Example 26

36. Rewrite the function using the power-reducing formulas.
Example 27

37. Write the trigonometric expression as an algebraic expression.
Example 28

38. HW #26 pg 396 ( odd)