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Pre-­‐Calculus Chapter 15-­‐17 Review 1. Convert 118˚44’15” to the decimal form of degrees. 3. Convert 150˚ to radians. Leave your answers in terms of π . 5. Convert 7. Convert 60 mph into a) ft/sec b) rad/sec (let r = 20in) c) RPM Name: _______________________ Period: _____ 2. Convert 99.37˚ to degrees, minutes, seconds. 4. Convert 71.72˚ into radians. 6. Convert 1.3 rad into degrees. 7π
into degress. 9
9. Find sine, cosine and tangent for 8. Convert 1.3 rad/sec into a) ft/sec (let r = 44 ft) b) MPH C) RPM 5π
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10. Find sine, cosine and tangent for −
3π
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11. Consider the figure below illustrating a region bounded by two circular arcs. The area of the striped region is 3920 square meters, z = 40 meters, and s = 126 meters. Find the value of r. The figure is not to scale. 12. You are measuring trees in a forest. Standing on the ground exactly half-­‐way between two trees, you measure the angle the top of each tree makes with the horizon: one angle is 67°, and the other is 82°. If one tree is 80 feet taller than the other, how far apart (horizontal distance along the ground) are the two trees? 13. Alexandra and Boris are running around a circular track. The track has a radius of 50 meters. Boris starts from the easternmost point of the track, and runs clockwise. Alexandra starts at the same time from the northernmost point of the track, and runs counter-­‐clockwise. Boris runs at a constant speed of 4 meters per second, and passes Alexandra for the first time after 20 seconds. (a) What is Alexandra’s speed in meters per second? (b) After running for 1000 seconds, who is farther south, Boris or Alexandra? Show all work. 14. Thinking about where x-­‐coordinates and y-­‐coordinates are positive and negative, label below which quadrants will have +/-­‐ sines, cosines, and tangents. sinθ (opp/hyp) cosθ (adj/hyp) tanθ (opp/adj) 15. Maria is riding a bicycle. The rear wheel has a radius of 34.3 cm, and the front sprocket has a radius of 8.7 cm. If she travels at a speed of 27 kilometers per hour when pedaling at a rate of 96 revolutions per minute, what is the radius of the rear sprocket? The figure may not be to scale. 16. Ron and Harry are both running counterclockwise on a circular track with radius 10 feet. Ron starts at the southernmost point and Harry is the easternmost point. Ron is running at 2 feet/sec and Harry completes one lap in 30 seconds. (a) Give Harry’s x and y coordinates after 3 seconds. (b) Give Ron’s x and y coordinates after 50 seconds. (c) Find the distance between Harry and Ron after they have been running for 50 seconds. 17. A Circular fountain is surrounded by flowers. The fountain’s diameter is 8 ft. The flowers extend 1.5 ft out from the fountain on all sides. What area do the flowers cover?
18. Maria is running around a circular track. She runs clockwise and, from when she starts, it takes her 28 seconds to reach the southernmost point of the track. She takes 105 seconds to run each lap of the track. (a) From when she starts, how long does it take her to reach the easternmost point of the track? (b) Bob starts running on the track at the same time as Maria. He starts from the northernmost point and runs counter-­‐clockwise. He takes 130 seconds to run each lap of the track. Let R be the radius of the track. Using a coordinate system with the origin at the center of the track, find Bob’s x-­‐ and y-­‐coordinates when he passes Maria for the first time (your answer will involve R). Answers: 1. 118.7375˚ 7.a) 88 ft/sec 9. s=-­‐√3/2 c=1/2 t=-­‐√3 16. a) (8.09, 5.88) 2. 90˚22’12” b) 52.8 rad/sec 10. s=-­‐√2/2 c=-­‐√2/2 t = 1 b) (-­‐5.44, 8.39) c) 504.2 RMP c) 13.76 feet 5π
3. 11. 90 meters 17. 44.8 ft2 6
4. 1.2518 rad 8. a) 57.2 ft/sec 12. 33.62 feet 18. a) 1.75 sec b) 12.41 RPM b)(−0.8356238R,−0.549302R) c) 39 MPH 5. 140˚ 13. a) 7.78097245 m/sec south. b) Alex is farther 6. 74.48˚ 15. The rear sprocket’s radius is 4 cm.