1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 1 Homework, Page 421 Find the exact value. 1.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 2 Homework, Page 421 Find the exact value. 5.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 3 Homework, Page 421 Find the exact value. 9.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 4 Homework, Page 421 Use a calculator to find the approximate value. Express the answer in degrees. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 5 Homework, Page 421 Use a calculator to find the approximate value. Express the answer in radians. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 6 Homework, Page 421 Describe the end behavior of the function. 21.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 7 Homework, Page 421 Find the exact value without a calculator. 25.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 8 Homework, Page 421 Find the exact value without a calculator. 29.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 9 Homework, Page 421 Analyze each function for domain, range, continuity, increasing or decreasing, symmetry, boundedness, extrema, asymptotes, and end behavior. 33.

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 10 Homework, Page 421 Use transformations to describe how the graph of the function is related to a basic inverse trigonometric graph. State the domain and range. 37.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 11 Homework, Page 421 Find an exact solution to the equation without a calculator. 41.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 12 Homework, Page 421 Find an exact solution to the equation without a calculator. 45.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 13 Homework, Page 421 Find an algebraic expression equivalent to the given expression. 49.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 14 Homework, Page 421 53.The bottom of a picture is 2 ft above eye level and the picture is 12 ft tall. Angle θ is formed by the lines of vision to the top and bottom of the picture. a. Show that

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 15 Homework, Page 421 53.b.Graph θ in a [0, 25] by [0, 50] viewing window using degree mode. Show that the maximum value of θ occurs approximately 5.3 ft from the picture. c.How far, to the nearest foot, are you standing if θ =35º? 2 ft or 15 ft

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 16 Homework, Page 421 57.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 17 Homework, Page 421 61. a. b. c. d. e.

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 18 Homework, Page 421 65. Graph each of the three functions and interpret the graph to find domain, range, and period. Which of these functions has points of discontinuity? Are the discontinuities removable or nonremovable? a. The function has a domain of all real numbers, a range of –π/2 to π/2, and a period of 2π.

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 19 Homework, Page 421 65. b. The function has domain of all real numbers, a range of 0 to π, and a period of 2π. c. The function has domain of all real numbers ≠ nπ/2, n≠0, a range of –π/2 to π/2, and a period of π. The discontinuities are not removable.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 20 Homework, Page 421 69. Use elementary transformations and the arctangent function to construct a function with a domain of all real numbers that has horizontal asymptotes at y = 24 and y = 42.

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4.8 Solving Problems with Trigonometry

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 22 Quick Review 1. Solve for a. a 3 23 º

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 23 Quick Review

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 24 Quick Review Solutions 1. Solve for a. a 3 23 º

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 25 Quick Review Solutions

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 26 What you’ll learn about More Right Triangle Problems Simple Harmonic Motion … and why These problems illustrate some of the better- known applications of trigonometry.

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 27 Angle of Elevation, Angle of Depression An angle of elevation is the angle through which the eye moves up from horizontal to look at something above. An angle of depression is the angle through which the eye moves down from horizontal to look at something below.

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 28 Example Using Angle of Elevation The angle of elevation from the buoy to the top of the Barnegat Bay lighthouse 130 feet above the surface of the water is 5 º. Find the distance x from the base of the lighthouse to the buoy. 130 x 5º5º

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 29 Example Using Angle of Depression An observer watches a car approach from the top of a 100-ft building. If the angle of depression of the car changes from 15º to 35º during the period of observation, how far did the car move?

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 30 Example Navigation Problem A hydrofoil travels at a speed of 40 knots from Fort Lauderdale on a course of 065º for two hours and then turns to a course of 155º for four more hours. What are the direction and distance from Fort Lauderdale to the hydrofoil after the six hours?

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 31 Example Navigation Problem Port A is directly east of Port B on Lake Wonderful. A police boat leaves Port B at 23 kts on a course of 095ºand a smuggler’s boat leaves Port A on a course of 195º at the same time. Two hours later the boats collide. How fast was the smuggler’s boat traveling? How far is port A from Port B?

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 32 Simple Harmonic Motion

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 33 Example Calculating Harmonic Motion A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 4 cm, find the modeling equation if it takes 3 seconds to complete one cycle.

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 34 Homework Homework Assignment #8 Review Section 4.8 Page 431, Exercises: 1 – 49 (EOO) Quiz next time