1. Homework, Page 460
Prove the algebraic identity. 1.

2. Homework, Page 460
Tell whether or not f (x) = sin x is an identity. 5.

3. Homework, Page 460
Tell whether or not f (x) = sin x is an identity. 9.

4. Homework, Page 460
Prove the identity.
13.

5. Homework, Page 460
Prove the identity.
17.

6. Homework, Page 460
Prove the identity.
21.

7. Homework, Page 460
Prove the identity.
25.

8. Homework, Page 460
Prove the identity.
29.

9. Homework, Page 460
Prove the identity.
33.

10. Homework, Page 460
Prove the identity.
37.

11. Homework, Page 460
Prove the identity.
41.

12. Homework, Page 460
Prove the identity.
45.

13. Homework, Page 460
Prove the identity.
45.

14. Homework, Page 460
Prove the identity.
49.

15. Homework, Page 460
Match the function with an equivalent expression, then confirm the matching with a proof. d.

16. Homework, Page 460
Match the function with an equivalent expression, then confirm the matching with a proof. b.

17. Homework, Page 460
61. Which of the following is a good first step in proving:
A. B.
C. D. E.

18. Homework, Page 460
Identify a simple function that has the same graph. Then confirm your answer with a proof.
65.

19. Homework, Page 460
Identify a simple function that has the same graph. Then confirm your answer with a proof.
69.

20. Homework, Page 460
Confirm the identity.
73.

21. Homework, Page 460
Confirm the identity.
77.

22. Sum and Difference Identities
5.3
Sum and Difference Identities

23. Quick Review

24. Quick Review Solutions

25. What you’ll learn about
Cosine of a Difference
Cosine of a Sum
Sine of a Difference or Sum
Tangent of a Difference or Sum
Verifying a Sinusoid Algebraically
… and why
These identities provide clear examples of how different the
algebra of functions can be from the algebra of real numbers.

26. Cosine of a Sum or Difference

27. Example Using the Cosine-of-a-Difference Identity

28. Sine of a Sum or Difference

29. Example Using the Sum and Difference Formulas

30. Tangent of a Difference of Sum

31. Example Proving an Identity

32. Example Proving a Reduction Formula

33. Example Expressing a Function as a Sinusoid

34. Example Proving an Identity

35. Homework
Homework Assignment #12
Read Section 5.4
Page 468, Exercises: 1 – 61 (EOO)
Quiz next time

36. Multiple-Angle Identities
5.4
Multiple-Angle Identities

37. Quick Review

38. Quick Review Solutions

39. 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.

40. Deriving Double-Angle Identities

41. Double Angle Identities

42. Example Solving a Problem Using double Angle Identities

43. Power-Reducing Identities

44. Example Reducing a Power of 4

45. Half-Angle Identities

46. Example Using a Double Angle Identity