1. Chapter 6 Applications of Trigonometry

2. 6.1 VECTORS IN THE pLANE

3. Quick Review

4. Quick Review

5. Quick Review Solutions

6. Quick Review Solutions

7. Directed Line Segment

8. Two-Dimensional Vector

9. Initial Point, Terminal Point, Equivalent

10. Find the vector for both
RS= <3,4>
QP= <3,4>

11. Magnitude

12. Example Finding Magnitude of a Vector

13. Example Finding Magnitude of a Vector

14. Find Vector
Find the magnitude of v represented by 𝑆𝑇 , where S=(2, -8) and T= (-3, 7)

15. Vector Addition and Scalar Multiplication

16. Example Performing Vector Operations

17. Example Performing Vector Operations

18. Group Work Let u=<-1,3> and v=<5, -6> Find A) u+v B) 3u
C) 2u+(-1)v

19. Unit Vectors

20. Example Finding a Unit Vector

21. Example Finding a Unit Vector

22. Find the unit vector
P=<3,9>
Q=<1, 6>

23. Standard Unit Vectors

24. Resolving the Vector

25. Example Finding the Components of a Vector

26. Example Finding the Components of a Vector

27. Example Finding the Direction Angle of a Vector

28. Example Finding the Direction Angle of a Vector

29. Velocity and Speed The velocity of a moving object is a vector
because velocity has both magnitude and
direction. The magnitude of velocity is speed.

30. Word Problem
The pilot pilots the plane from San Franciso due east. There is a 65 mph wind with the bearing 60 degrees (from the y-axis). Find the compass heading the pilot should follow, and determine what the airplane’s ground speed will be (assuming its speed with no wind is 450 mph).

31. Answer Bearing should be approx 94.14 degrees 𝜃=−4.14°
Speed is mph

32. Word Problem
A jet is flying on a bearing of 65° at 500 mph. Find the component form of the velocity of the airplane. Recall that the bearing is the angle that the line of travel makes with due north, measured clockwise.

33. Answer
<453.15,211.31>

34. Homework Practice
Pg 511 #1-45 eoo

35. Polar Coordinates

36. Quick Review

37. Quick Review
Use the Law of Cosines to find the measure of the third side of the given triangle. 4.
40º 8 10 5.
35º 6 11

38. Quick Review Solutions

39. Quick Review Solutions
Use the Law of Cosines to find the measure of the third side of the given triangle. 4.
40º 8 10 5.
35º 6 11
6.4 7

40. The Polar Coordinate System

41. Example Plotting Points in the Polar Coordinate System

42. Example Plotting Points in the Polar Coordinate System

43. Finding all Polar Coordinates of a Point

44. Coordinate Conversion Equations

45. Example Converting from Polar to Rectangular Coordinates

46. Example Converting from Polar to Rectangular Coordinates

47. Example Converting from Rectangular to Polar Coordinates

48. Example Converting from Rectangular to Polar Coordinates

49. Example Converting from Polar Form to Rectangular Form

50. Example Converting from Polar Form to Rectangular Form

51. Example Converting from Polar Form to Rectangular Form

52. Example Converting from Polar Form to Rectangular Form

53. 6.4 Polar Coordinates Page 537
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

54. 6.4 Polar Coordinates (cont’d)
Page 537
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

55. Homework Practice
Pg 539 #1-50 eoe

56. Limits and Motion: The tangent problem

57. Quick Review

58. Quick Review Solutions

59. What is Tangent?

60. Average Velocity Average velocity is the change in position
divided by the change in time.

61. Limits at a (Informal)

62. Example Finding the Slope of a Tangent Line

63. Example Finding the Slope of a Tangent Line

64. Example:
A ball rolls down a ramp so that its distance s from the top of the ramp after t seconds is exactly feet. What is its instantaneous velocity after 3 second?

65. Average Rate of Change

66. Derivative at a Point

67. Derivative at a Point (easier for computing)

68. Example Finding a Derivative at a Point

69. Example Finding a Derivative at a Point

70. Derivative

71. Example Finding the Derivative of a Function

72. Example Finding the Derivative of a Function

73. Example:
Find if

74. Example:
Find if

75. Homework Practice
P 801 #1-32 eoe

76. Integral: The area problem

77. Quick Review

78. Quick Review Solutions

79. Example Computing Distance Traveled
A car travels at an average rate of 56 miles per hour for 3 hours
and 30 minutes. How far does the car travel?

80. Example Computing Distance Traveled
A car travels at an average rate of 56 miles per hour for 3 hours
and 30 minutes. How far does the car travel?

81. Limits at Infinity (Informal)

83. Definite Integral