1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 1

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter 10 Parametric, Vector, and Polar Functions

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 10.1 Parametric Functions

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 4 Quick Review

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 5 Quick Review Solutions

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 6 What you’ll learn about Parametric Curves in the Plane Slope and Concavity Arc Length Cycloids …and why Parametric equations enable us to define some interesting and important curves that would be difficult or impossible to define in the form y=f(x).

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 7 Example Reviewing Some Parametric Curves

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 8 Example Reviewing Some Parametric Curves

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 9 Parametric Differentiation Formulas

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 10 Example Analyzing a Parametric Curve

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 11 Example Analyzing a Parametric Curve

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 12 Arc Length of a Parametrized Curve

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 13 Example Measuring a Parametric Curve

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 14 Cycloids

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 10.2 Vectors in the Plane

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 16 Quick Review

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 17 Quick Review

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 18 Quick Review Solutions

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 19 Quick Review Solutions

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 20 What you’ll learn about Two-Dimensional Vectors Vector Operations Modeling Planar Motion Velocity, Acceleration, and Speed Displacement and Distance Traveled …and why The jump from one to two dimensions (and eventually higher) is easier than one might think, thanks to the mathematics of vectors.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 21 Two-Dimensional Vectors

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 22 Magnitude of a Vector

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 23 Direction Angle of a Vector

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 24 Head Minus Tail (HMT) Rule

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 25 Example Finding Magnitude and Direction

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 26 Vector Addition and Scalar Multiplication

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 27 Example Performing Operations on Vectors

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 28 Properties of Vector Operations

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 29 Example Finding Ground Speed and Direction

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 30 Velocity, Speed, Acceleration, and Direction of Motion

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 31 Displacement and Distance Traveled

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 32 Example Finding Displacement and Distance Traveled

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 10.3 Polar Functions

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 34 Quick Review

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 35 Quick Review

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 36 Quick Review Solution

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 37 Quick Review Solutions

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 38 What you’ll learn about Polar Coordinates Polar Curves Slopes of Polar Curves Areas Enclosed by Polar Curves A Small Polar Gallery …and why Polar equations enable us to define some interesting and important curves that would be difficult or impossible to define in the form y=f(x).

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 39 Example Rectangular and Polar Coordinates

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 40 Example Rectangular and Polar Coordinates

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 41 Polar-Rectangular Conversion Formulas

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 42 Parametric Equations of Polar Curves

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 43 Example Finding Slope of a Polar Curve

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 44 Area in Polar Coordinates

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 45 Example Finding Area

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 46 Area Between Polar Curves

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 47 Circles

48. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 48 Rose Curves

49. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 49 Limaçon Curves

50. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 50 Lemniscate Curves

51. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 51 Spiral of Archimedes

52. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 52 Quick Quiz Sections 10.1 – 10.3

53. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 53 Quick Quiz Sections 10.1 – 10.3

54. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 54 Quick Quiz Sections 10.1 – 10.3

55. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 55 Quick Quiz Sections 10.1 – 10.3

56. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 56 Quick Quiz Sections 10.1 – 10.3

57. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 57 Quick Quiz Sections 10.1 – 10.3

58. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 58 Chapter Test

59. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 59 Chapter Test

60. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 60 Chapter Test Solutions

61. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 61 Chapter Test Solutions