SECTION 6.1 Angles, Arc Length, and Circular Motion 393 In Problems 47–52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. 47. 17° 48. 73° 49. 40 − ° 50. 51 − ° 51. 125° 52. 350° In Problems 53–58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places. 53. 3.14 54. 0.75 55. 7 56. 3 57. 9.28 58. 2 In Problems 59–64, convert each angle to a decimal in degrees. Round your answer to two decimal places. 59. 40 10 25 ° ′ ′′ 60. 61 42 21 ° ′ ′′ 61. 50 14 20 ° ′ ′′ 62. 73 40 40 ° ′ ′′ 63. 9 9 9 ° ′ ′′ 64. 98 22 45 ° ′ ′′ In Problems 65–70, convert each angle to D M S ° ′ ′′ form. Round your answer to the nearest second. 65. 40.32° 66. 61.24° 67. 18.255° 68. 29.411° 69. 19.99° 70. 44.01° In Problems 71–78, s denotes the length of the arc of a circle of radius r subtended by the central angle .θ Find the missing quantity. Round answers to three decimal places. 71. r s 10meters, 1 2 radian, ? θ = = = 72. r s 6feet, 2radians, ? θ = = = 73. s r 2 3 radian, 8feet, ? θ = = = 74. s r 1 4 radian, 6 centimeters, ? θ = = = 75. r s 10miles, 9miles, ? θ = = = 76. r s 6meters, 8meters, ? θ = = = 77. r s 2 inches, 30 , ? θ = = ° = 78. r s 3meters, 120 , ? θ = = ° = In Problems 79–86, A denotes the area of the sector of a circle of radius r formed by the central angle .θ Find the missing quantity. Round answers to three decimal places. 79. r A 10meters, 1 2 radian, ? θ = = = 80. r A 6feet, 2radians, ? θ = = = 81. A r 1 3 radian, 2 square feet, ? θ = = = 82. A r 1 4 radian, 6 square centimeters, ? θ = = = 83. r A 5miles, 3 square miles, ? θ = = = 84. r A 6meters, 8 square meters, ? θ = = = 85. r A 2 inches, 30 , ? θ = = ° = 86. r A 3meters, 120 , ? θ = = ° = In Problems 87–90, find the length s and the area A. Round answers to three decimal places. 87. 2 ft A 3 p s 88. 4 m A 6 p s 89. 12 yd 70˚ A s 90. 9 cm A s 50˚ Applications and Extensions 91. Movement of a Minute Hand The minute hand of a clock is 6 inches long. How far does the tip of the minute hand move in 15 minutes? How far does it move in 25 minutes? Round answers to two decimal places. 92. Movement of a Pendulum A pendulum swings through an angle of 20° each second. If the pendulum is 40 inches long, how far does its tip move each second? Round answers to two decimal places. 93. Area of a Sector Find the area of the sector of a circle of radius 4 meters formed by an angle of 45 .° Round the answer to two decimal places. 94. Area of a Sector Find the area of the sector of a circle of radius 3 centimeters formed by an angle of 60 .° Round the answer to two decimal places. 95. Watering a Lawn A water sprinkler sprays water over a distance of 30 feet while rotating through an angle of 135 .° What area of lawn receives water? 30 ft 135˚ 12 1 2 3 4 5 6 7 8 9 10 2 11
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