1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 1 Homework, Page 381 Identify the one angle that is not coterminal with the others. 1.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 2 Homework, Page 381 Evaluate the six trigonometric functions of the angle θ. 5.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 3 Homework, Page 381 Point P is on the terminal side of angle θ. Evaluate the six trigonometric functions for θ. If the function is undefined, write undefined. 9.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 4 Homework, Page 381 State the sign (+ or –) of (a) sin t, (b) cos t (c) tan t for values of t in the interval given. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 5 Homework, Page 381 Determine the sign (+ or –) of the given value without a calculator. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 6 Homework, Page 381 Choose the point on the terminal side of θ. 21. (a) (2, 2) (b) (c) Choice (a) as tan 45º = 1.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 7 Homework, Page 381 Evaluate without using a calculator by using ratios in a reference triangle. 25.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 8 Homework, Page 381 Evaluate without using a calculator by using ratios in a reference triangle. 29.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 9 Homework, Page 381 Evaluate without using a calculator by using ratios in a reference triangle. 33.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 10 Homework, Page 381 Find (a) sin θ, (b) cos θ, and (c) tan θ for the given quadrantal angle. If the value is undefined, write undefined. 37.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 11 Homework, Page 381 Find (a) sin θ, (b) cos θ, and (c) tan θ for the given quadrantal angle. If the value is undefined, write undefined. 41.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 12 Homework, Page 381 Evaluate without using a calculator. 45.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 13 Homework, Page 381 Evaluate by using the period of the function. 49.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 14 Homework, Page 381 53. Use your calculator to evaluate the expressions in Exercises 49 – 52. Does your calculator give the correct answer. Many miss all four. Give a brief explanation why. The calculator algorithms apparently do recognize large multiples of pi and end up evaluating at nearby values.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 15 Homework, Page 381 57. A weight suspended from a spring is set into motion. Its displacement d from equilibrium is modeled by the equation where d is the displacement in inches and t is the time in seconds. Find the displacement at the given time. (a) t = 0 (b)t = 3

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 16 Homework, Page 381 61. If θ is an angle in a triangle such that cos θ < 0, then θ is an obtuse angle. Justify your answer. True. An obtuse angle in the standard position would have its terminal side in the second quadrant and cosine is negative in the second quadrant.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 17 Homework, Page 381 65. The range of the function a.[1] b.[-1, 1] c.[0, 1] d.[0, 2] e.[0, ∞]

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 18 Homework, Page 381 Find the value of the unique real number θ between 0 and 2π that satisfies the two given conditions. 69. If tan and sin are negative, cos must be positive. The angle must be in the fourth quadrant and the reference angle is π/4, so θ = 2π – π/4 = 7π/4

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

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 20 What you’ll learn about The Basic Waves Sinusoids and Transformations Modeling Periodic Behavior with Sinusoids … and why Sine and cosine gain added significance when used to model waves and periodic behavior.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Leading Questions A function is a sinusoid if it can be written in the form y = a sin (bx + c) +d, where a and b ≠ 0. The function y = a cos (bx + c) +d is not a sinusoid. The amplitude of a sinusoid is |a|. The period of a sinusoid is |b|/2π. The frequency of a sinusoid is |b|/2π. Sinusoids are often used to model the behavior of periodic occurrences. Slide 4- 21

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 22 Sinusoid

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 23 Amplitude of a Sinusoid

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 24 Example Finding Amplitude Find the amplitude of each function and use the language of transformations to describe how the graphs are related. (a) (b) (c)

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 25 Period of a Sinusoid

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 26 Example Finding Period and Frequency Find the period and frequency of each function and use the language of transformations to describe how the graphs are related. (a) (b) (c)

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 27 Example Horizontal Stretch or Shrink and Period

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 28 Frequency of a Sinusoid

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 29 Example Combining a Phase Shift with a Period Change

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 30 Graphs of Sinusoids

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 31 Constructing a Sinusoidal Model using Time

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 32 Constructing a Sinusoidal Model using Time

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 33 Example Constructing a Sinusoidal Model

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 34 Example Constructing a Sinusoidal Model

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Following Questions The period of the tangent function is 2π. Tangent is an odd function. Cotangent is an even function. The graph of cosecant has relative minimum values, but no absolute minimum value. Some trig equations may be solved algebraically. Most trig equations may be solved graphically. Slide 4- 35

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 36 Homework Homework Assignment #29 Read Section 4.5 Page 392, Exercises: 1 – 89 (EOO)

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

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 38 Quick Review

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 39 Quick Review Solutions

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 40 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.

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 41 Asymptotes of the Tangent Function

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 42 Zeros of the Tangent Function

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 43 Asymptotes of the Cotangent Function

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 44 Zeros of the Cotangent Function

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 45 The Secant Function

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 46 The Cosecant Function

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 47 Basic Trigonometry Functions

48. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 48 Example Analyzing Trigonometric Functions Analyze the function for domain, range, continuity, increasing or decreasing, symmetry, boundedness, extrema, asymptotes, and end behavior

49. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 49 Example Transformations of Trigonometric Functions Describe the transformations required to obtain the graph of the given function from a basic trigonometric function.

50. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 50 Example Solving Trigonometric Equations Solve the equation for x in the given interval.

51. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 51 Example Solving Trigonometric Equations With a Calculator Solve the equation for x in the given interval.

52. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 52 Example Solving Trigonometric Word Problems A hot air balloon is being blow due east from point P and traveling at a constant height of 800 ft. The angle y is formed by the ground and the line of vision from point P to the balloon. The angle changes as the balloon travels. a. Express the horizontal distance x as a function of the angle y. b. When the angle is, what is the horizontal distance from P? c. An angle of is equivalent to how many degrees?