562 CHAPTER 5 Trigonometric Functions 112. csc 145° 45′ 113. cot 183° 48′ 114. tan421° 30′ 115. sin1-312° 12′2 116. tan1-80° 06′2 117. csc1-317° 36′2 118. cot1-512° 20′2 119. 1 cot 23.4° 120. 1 sec 14.8° 121. cos 77° sin77° 122. sin33° cos 33° Find a value of u in the interval 30°, 90°2 that satisfies each statement. Write each answer in decimal degrees to six decimal places. See Example 9. 123. tanu = 1.4739716 124. tanu = 6.4358841 125. sinu = 0.27843196 126. sinu = 0.84802194 127. cot u = 1.2575516 128. csc u = 1.3861147 129. sec u = 2.7496222 130. sec u = 1.1606249 131. cos u = 0.70058013 132. cos u = 0.85536428 133. csc u = 4.7216543 134. cot u = 0.21563481 (Modeling) Grade Resistance Solve each problem. See Example 10. 135. Find the grade resistance, to the nearest ten pounds, for a 2100-lb car traveling on a 1.8° uphill grade. 136. Find the grade resistance, to the nearest ten pounds, for a 2400-lb car traveling on a -2.4° downhill grade. 137. A 2600-lb car traveling downhill has a grade resistance of -130 lb. Find the angle of the grade to the nearest tenth of a degree. 138. A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree. 139. A car traveling on a 2.7° uphill grade has a grade resistance of 120 lb. Determine the weight of the car to the nearest hundred pounds. 140. A car traveling on a -3° downhill grade has a grade resistance of -145 lb. Determine the weight of the car to the nearest hundred pounds. 141. Which has the greater grade resistance: a 2200-lb car on a 2° uphill grade or a 2000-lb car on a 2.2° uphill grade? 142. Complete the table for values of sinu, tanu, and pu 180 to four decimal places. U 0° 0.5° 1° 1.5° 2° 2.5° 3° 3.5° 4° sinU tanU PU 180 (a) How do sinu, tanu, and pu 180 compare for small grades u? (b) Highway grades are usually small. Give two approximations of the grade resistance F = Wsinu that do not use the sine function. (c) A stretch of highway has a 4-ft vertical rise for every 100 ft of horizontal run. Use an approximation from part (b) to estimate the grade resistance, to the nearest pound, for a 2000-lb car on this stretch of highway. (d) Without evaluating a trigonometric function, estimate the grade resistance, to the nearest pound, for an 1800-lb car on a stretch of highway that has a 3.75° grade.
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