602 CHAPTER 6 The Circular Functions and Their Graphs 65. Concept Check The figure shows the same angles measured in both degrees and radians. Complete the missing measures. ____°; radians 180°; ____ radians 0°; 0 radians 30°; ____ radian 60°; ____ radians ____°; radian 90°; radians 270°; radians ____°; radians 4p__ 3 2p__ 3 p_ 2 p_ 4 3p__ 2 5p__ 3 3p__ 4 225°; ____ radians 210°; ____ radians 150°; ____ radians ____°; radians ____°; radians 315°; ____ radians 330°; ____ radians y x Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 4. 75. Panama City, Panama, 9° N, and Pittsburgh, Pennsylvania, 40° N 76. Farmersville, California, 36° N, and Penticton, British Columbia, 49° N 77. New York City, New York, 41° N, and Lima, Peru, 12° S 78. Halifax, Nova Scotia, 45° N, and Buenos Aires, Argentina, 34° S 79. Latitude of Madison Madison, South Dakota, and Dallas, Texas, are 1200 km apart and lie on the same north-south line. The latitude of Dallas is 33° N. What is the latitude of Madison? 80. Latitude of Toronto Charleston, South Carolina, and Toronto, Canada, are 1100 km apart and lie on the same north-south line. The latitude of Charleston is 33° N. What is the latitude of Toronto? 66. Concept Check What is the exact radian measure of an angle measuring p degrees? Unless otherwise directed, give calculator approximations in answers in the rest of this exercise set. Find the length to three significant digits of each arc intercepted by a central angle u in a circle of radius r. See Example 3. 67. r = 12.3 cm, u = 2p 3 radians 68. r = 0.892 cm, u = 11p 10 radians 69. r = 1.38 ft, u = 5p 6 radians 70. r = 3.24 mi, u = 7p 6 radians 71. r = 4.82 m, u = 60° 72. r = 71.9 cm, u = 135° 73. r = 15.1 in., u = 210° 74. r = 12.4 ft, u = 330° Work each problem. See Examples 5 and 6. 81. Gear Movement Two gears are adjusted so that the smaller gear drives the larger one, as shown in the figure. If the smaller gear rotates through an angle of 300°, through how many degrees does the larger gear rotate? 3.7 cm 7.1 cm
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