Homework, Page 356

1. Homework, Page 356 Convert from DMS to decimal form. 1.

2. Homework, Page 356 Convert from decimal form to DMS. 5.

3. Homework, Page 356 Convert from decimal or DMS to radians. 9.

4. Homework, Page 356 Convert from decimal or DMS to radians. 13.

5. Homework, Page 356 Convert from radians to degrees. 17.

6. Homework, Page 356 Convert from radians to degrees. 21.

7. Homework, Page 356 Use the appropriate arc length formula to find the missing information. 25.

8. Homework, Page 356 Use the appropriate arc length formula to find the missing information. 29.

9. Homework, Page 356 A central angle θ intercepts arcs s1 and s2 on two concentric circles with radii r1 and r2, respectively. Find the missing information. 33.

10. Homework, Page 356 37. It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track?

11. Homework, Page 356 41. Which compass bearing is closest to a bearing of 121º?

12. Homework, Page 356 45. Cathy Nyugen races on a bicycle with 13-inch radius wheels. When she is traveling at a speed of 44 ft/sec, how many revolutions per minute are her wheels making?

13. Homework, Page 356 49. The captain of the tourist boat Julia follows a 038º course for 2 miles and then changes course to 047º for the next 4 miles. Draw a sketch of this trip.

14. Homework, Page 356 53. A simple pulley with the given radius r used to lift heavy objects is positioned 10 feet above ground level. Given the pulley rotates θº, determine the height to which the object is lifted. a. r = 4 in, θ = 720º b. r = 2 ft, θ = 180º

15. Homework, Page 356 57. If horse A is twice as far as horse B from the center of a merry-go-round, then horse A travels twice as fast as horse B. Justify your answer. True, since all points on a given radius have the same angular displacement, horse A will travel twice as far as horse B for the same angular displacement, thereby traveling twice as fast.

16. Homework, Page 356 61. A bicycle with 26-inch diameter wheels is traveling at 10 mph. To the nearest whole number, how many revolutions does each wheel make per minute? a. 54 b. 129 c. 259 d. 406 e. 646

17. Homework, Page 356 Find the difference in longitude between the given cities. 65. Minneapolis and Chicago

18. Homework, Page 356 Assume the cities have the same longitude and find the distance between them in nautical miles. 69. New Orleans and Minneapolis

19. Homework, Page 356 73. Control tower A is 60 miles east of control tower B. At a certain time, an airplane bears 340º from control tower A and 037º from control tower B. Use a drawing to model the exact location of the airplane.

20. 4.2 Trigonometric Functions of Acute Angles

21. x 2 3 6 x 3 Quick Review 1. Solve for x. 2. Solve for x.

22. Quick Review

23. x 2 3 6 x 3 Quick Review Solutions 1. Solve for x. 2. Solve for x.

24. Quick Review Solutions

25. What you’ll learn about • Right Triangle Trigonometry • Two Famous Triangles • Evaluating Trigonometric Functions with a Calculator • Applications of Right Triangle Trigonometry … and why The many applications of right triangle trigonometry gave the subject its name.

26. Leading Questions The functions y = secant x and y = cosecant x are reciprocal functions. Given the values of two primary trig functions, we can calculate the values of the others. Our left hand provides a key to the basic trig functions that is always with us. Given one angle and one side of a right triangle, we can find the other angle and sides.

27. Standard Position An acute angle θ in standard position, with one ray along the positive x-axis and the other extending into the first quadrant.

28. Trigonometric Functions

29. Example Evaluating Trigonometric Functions of 45º Find the values of all six trigonometric functions for an angle of 45º.

30. Example Evaluating Trigonometric Functions of 60º Find the values of all six trigonometric functions for an angle of 60º.

31. Example Evaluating Trigonometric for General Triangles Find the values of all six trigonometric functions for the angle x in the triangle shown.

32. Trigonometric Functions of Five Common Angles

33. Trig Value Memory Aid

34. Common Calculator Errors When Evaluating Trig Functions • Using the calculator in the wrong angle mode (degree/radians) • Using the inverse trig keys to evaluate cot, sec, and csc • Using function shorthand that the calculator does not recognize • Not closing parentheses

35. Example Evaluating Trigonometric for General Triangles Find the exact value of the sine of 60º.

36. Example Solving a Right Triangle

37. Example Solving a Word Problem

38. Following Questions The circular functions get their name from the fact that we go around in circles trying to understand them. Angles are commonly measured counterclock-wise from the initial side to the terminal side. Periods of functions are concerned with the frequency of their repetition. A unit circle has a diameter of one and is located wherever convenient.

39. Homework • Review Section 4.2 • Page 366, Exercises: 1 – 73 (EOO)

40. 4.3 Trigonometry Extended: The Circular Functions

41. Quick Review

42. Quick Review Solutions

43. What you’ll learn about • Trigonometric Functions of Any Angle • Trigonometric Functions of Real Numbers • Periodic Functions • The 16-point unit circle … and why Extending trigonometric functions beyond triangle ratios opens up a new world of applications.

44. Initial Side, Terminal Side

45. Positive Angle, Negative Angle

46. Coterminal Angles Two angles in an extended angle-measurement system can have the same initial side and the same terminal side, yet have different measures. Such angles are called coterminal angles.

47. Example Finding Coterminal Angles

48. Example Finding Coterminal Angles

49. Example Evaluating Trig Functions Determined by a Point in Quadrant I

50. Trigonometric Functions of any Angle