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c Math 150 WIR, Fall 2008, Benjamin Aurispa Math 150 Week in Review 8 Problem Set 1. (a) Express 200◦ in radians. (b) Express 5π 4 radians in degrees. 2. An arc of length 6 ft subtends a central angle of 20◦ . What is the radius of this circle? 3. In a pizza with diameter 16 in, the area of a certain piece is 24 in2 . What is the length of the crust on this piece? 4. If a record player makes 8 revolutions every 5 seconds, what is the angular speed of the player? 1 c Math 150 WIR, Fall 2008, Benjamin Aurispa 5. A car tire has a radius of 12 inches. The tire is rotating at a rate of 700 rpm. What is the speed of the car? (What is the linear speed of the tire?) 6. Find coterminal angles between 0◦ and 360◦ or 0 and 2π for the following. (a) −680◦ (b) 43π 7 7. A water slide at a water park forms an angle of elevation of 10◦ from the water to the top of the slide. The endpoint of the slide is 110 ft horizontally from the start of the slide. (a) How long is the slide? (b) How high does the slide start? 2 c Math 150 WIR, Fall 2008, Benjamin Aurispa 8. An ant is sitting between 2 towers. One tower is 100 ft tall and the other is 150 ft tall. The angle of depression from the 100 ft tower to the ant is 32◦ . The angle of elevation from the ant to the top of the 150 ft tower is 43◦ . How far apart are the towers? 9. Find the reference angle for the given angle and then evaluate the trig function exactly. (a) csc(−315◦ ) (b) sec 4π 3 (c) tan 690◦ 3 c Math 150 WIR, Fall 2008, Benjamin Aurispa 10. Given that csc θ = 7 4 and that cot θ < 0, find the other trig functions for θ. 11. Solve the following triangles. (a) A = 90◦ , B = 15◦ , c = 4 (b) C = 42◦ , b = 19, c = 22 4 c Math 150 WIR, Fall 2008, Benjamin Aurispa (c) A = 15◦ , C = 110◦ , b = 10 (d) B = 37◦ , a = 12, b = 9 5 c Math 150 WIR, Fall 2008, Benjamin Aurispa 12. How many triangles exist that satisfy the following? (a) A = 65◦ , a = 60, c = 75 (b) B = 107◦ , c = 21, b = 15 (c) C = 99◦ , a = 51, c = 61 13. A ski lift takes people to the top of a mountain. The pickup point for the ski lift is 5000 ft from the base of the mountain. The angle of elevation from the pickup point to the top of the mountain is 22◦ and the angle of elevation from the base of the mountain to the top of the mountain is 64◦ . (a) What is the distance the ski lift travels? (b) What is the vertical height of the mountain? 6