673 CHAPTER 6 Review Exercises Find a calculator approximation to four decimal places for each circular function value. 37. sin 1.0472 38. tan 1.2275 39. cos1-0.24432 40. cot 3.0543 41. sec 7.3159 42. csc 4.8386 Find the approximate value of s, to four decimal places, in the interval C 0, p 2 D that makes each statement true. 43. cos s = 0.9250 44. tan s = 4.0112 45. sin s = 0.4924 46. csc s = 1.2361 47. cot s = 0.5022 48. sec s = 4.5600 Find the exact value of s in the given interval that has the given circular function value. 49. c 0, p 2 d ; cos s = 22 2 50. c p 2 , pd ; tan s = -23 51. c p, 3p 2 d ; sec s = - 223 3 52. c 3p 2 , 2pd ; sin s = - 1 2 Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed v. Use the given values of r, v, and t to do the following. (a) Find the angle generated by P in time t. (b) Find the distance traveled by P along the circle in time t. (c) Find the linear speed of P. 53. r = 15 cm, v = 2p 3 radians per sec, t = 30 sec 54. r = 45 ft, v = p 36 radian per min, t = 12 min Solve each problem. 55. Linear Speed of a Flywheel Find the linear speed of a point on the edge of a flywheel of radius 7 cm if the flywheel is rotating 90 times per sec. 56. Angular Speed of a Ferris Wheel A Ferris wheel has radius 25 ft. A person takes a seat, and then the wheel turns 5p 6 radians. (a) How far is the person above the ground to the nearest foot? (b) If it takes 30 sec for the wheel to turn 5p 6 radians, what is the angular speed of the wheel? 57. (Modeling) Archaeology An archaeology professor believes that an unearthed fragment is a piece of the edge of a circular ceremonial plate and uses a formula that will give the radius of the original plate using measurements from the fragment, shown in Figure A. Measurements are in inches. In Figure B, a is 1 2 the length of chord NP, and b is the distance from the midpoint of chord NP to the circle. According to the formula, the radius r of the circle, OR, is given by r = a2 + b2 2b . What is the radius of the original plate from which the fragment came? 0.2 1.4 1.4 Figure A N R P M Q O b a c 2 Figure B
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