 # Review Exercises 4.1 1. Find the radian measure of the central an...

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Review Exercises 4.1 1. Find the radian measure of the central angle of a circle of radius 6 centimeters that intercepts an arc of length 27 centimeters. In Exercises 2-4, convert each angle in degrees to radians. Express your answer as a multiple of TT. 2) 15° 3. 120° 4. 315 In Exercises 5-7, convert each angle in radians to degrees. 5m 3 7z 6. 5 7. 5r 6 In Exercises 8-12, draw each angle in standard position. 6 9.-23 10. 87 3 11.190° 12.-135° - In Exercises 13-17, find a positive angle less than 360' or 27r that is coterminal with the given angle. 13. 400° 14. -445° 15. 13% 4 16. 31x 6 17. 8m 3 18. Find the length of the arc on a circle of radius 10 feet intercepted by a 135° central angle. Express arc length in terms of TT. Then round your answer to two decimal places. 19 The angular speed of a propeller on a wind generator is 10.3 revolutions per minute. Express this angular speed in radians per minute. 20. The propeller of an airplane has a radius of 3 feet. The propeller is rotating at 2250 revolutions per minute. Find the linear speed, in feet per minute, of the tip of the propeller. 4.2 In Exercises 21-22, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t. In Exercises 21-22, a point P(x, y) is shown on the unit circle corresponding to a real numbert. Find the values of the trigonometric functions at t. y I 21) x (1.0) P=1-1-11 22. xd (1.0) p=12-13 In Exercises 23-26, use the figure shown to find the value of each trigonometric function at the indicated real number or state that the expression is undefined. y 3 1 V3 2 2 2 (0.1) V3 1 2 2 116 V3 2 . 1/2 2 xd (-1,0) (1.0) V3 . 1 V3 1 2 2 2 2 (0.-1) 1 - 2' V3 2 11-43 5% 23. sec 6 24. tan 4x 3 25. sec II 2 26.cot TO 27 If sin t = use identities to find the remaining trigonometric functions. 257 In Exercises 28-30 evaluate each expression without using a calculator. 28. tan 4.7 cot 4.7 29)sin² Il + cos² il 30. tan2 1.4 - sec2 1.4 Chapter 4 Trigonometric Functions > Review Exercises 4.3 31. Use the triangle to find each of the six trigonometric functions of 0. B 5 A 8 C In Exercises 32-35, find the exact value of each expression. Do not use a calculator. 32. 33. 34. 25-tan"= 35. cos 2= sec"= In Exercises 36-37, find a cofunction with the same value as the given expression. 36. sin 70 . 37 cos * 2 In Exercises 38-40, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number. B 38. a 23° A 100 mm C B 39, c 20 cm 61° o A C B 50 in. 40. a 48° C A 41. Ifsin 9 = 1/4 and 0 is acute, find tan (=-0). 42. A hiker climbs for a half mile up a slope whose inclination is 17° How many feet of altitude, to the nearest foot, does the hiker gain? 43. To find the distance across a lake, a surveyor took the measurements in the figure shown. What is the distance across the lake? Round to the nearest meter. is as to és < s 32° it 50 m 44. When a six-foot pole casts a four-foot shadow, what is the angle of elevation of the sun? Round to the nearest whole degree. 4.4 In Exercises 45-46, a point on the terminal side of angle 0 is given. Find the exact value of each of the six trigonometric functions of 0, or state that the function is undefined. 45. (-1,-5) 46. (0,-1) In Exercises 47-48, let 8 be an angle in standard position. Name the quadrant in which 0 lies. 47. itan 0 > 0 and sec 0 > 0 48. tan 0 > 0 and cos 0 < 0 In Exercises 49-51, find the exact value of each of the remaining trigonometric functions of 0. 49. cos 0 = 1/15 sin 0 < 0 50, tan 0 = - 51. cot 0 In Exercises 52-56, find the reference angle for each angle. 52. 265' 53. 5% 8 54. - 410 55. 17x 6 56. 11% 3 In Exercises 57-67, find the exact value of each expression. Do not use a calculator. 57. sin 240* 58. tan 120' 7= 59. sec 4 60. COS 11x 6 61. cot ( -210°) - 62. CSC =) 63. sin ( ) 64. sin 495' 65. tan 13* 4 66. sin 22.T 3 67.cos ( 355) 4.5 in Exercises 68-73, determine the amplitude and period of each function. Then graph one period of the function. 68. y = 3 sin 4x 69.y=-2 cos 2x 70. y = 2 cos x

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