1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4.4 Graphs of Sine and Cosine: Sinusoids

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 3 Quick Review Solutions

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 4 What you’ll learn about The Basic Waves Revisited Sinusoids and Transformations Modeling Periodic Behavior with Sinusoids … and why Sine and cosine gain added significance when used to model waves and periodic behavior.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 5 Sinusoid

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 6 Amplitude of a Sinusoid

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 7 Period of a Sinusoid

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 8 Example Horizontal Stretch or Shrink and Period

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 9 Example Horizontal Stretch or Shrink and Period

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 10 Frequency of a Sinusoid

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 11 Example Combining a Phase Shift with a Period Change

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 12 Example Combining a Phase Shift with a Period Change

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 13 Graphs of Sinusoids

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 14 Constructing a Sinusoidal Model using Time

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4.5 Graphs of Tangent, Cotangent, Secant, and Cosencant

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 16 Quick Review

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 17 Quick Review Solutions

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 18 What you’ll learn about The Tangent Function The Cotangent Function The Secant Function The Cosecant Function … and why This will give us functions for the remaining trigonometric ratios.

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 19 Asymptotes of the Tangent Function

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 20 Zeros of the Tangent Function

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 21 Asymptotes of the Cotangent Function

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 22 Zeros of the Cotangent Function

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 23 The Secant Function

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 24 The Cosecant Function

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 25 Basic Trigonometry Functions

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4.6 Graphs of Composite Trigonometric Functions

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 27 Quick Review

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 28 Quick Review Solutions

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 29 What you’ll learn about Combining Trigonometric and Algebraic Functions Sums and Differences of Sinusoids Damped Oscillation … and why Function composition extends our ability to model periodic phenomena like heartbeats and sound waves.

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 30 Example Combining the Cosine Function with x 2

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 31 Example Combining the Cosine Function with x 2

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 32 Example Combining the Cosine Function with x 2

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 33 Example Combining the Cosine Function with x 2

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 34 Sums That Are Sinusoids Functions

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 35 Example Identifying a Sinusoid

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 36 Example Identifying a Sinusoid

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 37 Example Identifying a Sinusoid

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 38 Example Identifying a Sinusoid

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 39 Damped Oscillation