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PRE-CALCULUS WORKSHEET 4.1 – 4.4 NAME CONVERT EACH ANGLE TO RADIANS. EXPRESS YOUR ANSWER AS A MULTIPLE OF . 1. 18° 2. 300° 3. -225° 6. -3 CONVERT EACH ANGLE TO DEGREES. 4. 9 5. 7 6 STATE THE QUADRANT IN WHICH EACH ANGLE LIES GIVEN IT IS IN STANDARD POSITION 7. 14 3 8. 780° 9. -380° FIND A POSITIVE ANGLE LESS THAN 360° OR 2 THAT IS COTERMINAL WITH THE GIVEN ANGLE. 10. 415° 11. 17 5 12. -765° FIND THE LENGTH OF THE ARC ON A CIRCLE OF RADIUS r INTERECEPTED BY A CENTRAL ANGLE . EXPRESS ARC LENGTH IN TERMS OF . 13. r = 12 inches, = 45° 14. r = 9 yards, = 315° 15. The minute hand of a clock moves from 12 to 2 o’clock, or 1 of a complete revolution. (A) Through 6 how many degrees does it move? (B) Through how many radians does it move? 16. The minute hand of a clock is 6 inches long and moves from 12 to 4 o’clock. How far does the tip of the minute hand move? Express your answer in terms of . [Hint: Find the arc length.] 17. Find the angular velocity in radians per second of the second hand of a clock. Express the answer in terms of . Show work. 18. Calculate the angular velocity in radians per minute of a Ferris wheel with a diameter of 208 feet that takes 25 seconds to rotate once. Express the answer in terms of . Show work. 19. If you sat on the rim of the Ferris wheel in #18, what would your linear velocity be, to the nearest foot per minute. Show work. 20. A flywheel mounted on an engine crankshaft has a radius of 6 inches. If the engine is running at 2800 rpm, what is the linear velocity of a point on the outer edge of the flywheel in feet per second? Show work. USE EVEN AND ODD PROPERTIES OF TRIGONOMETRIC FUNCTIONS AND YOUR ANSWER FROM (A) TO FIND THE ANSWER TO (B). 21. (A) cos 3 22. (B) cos 3 (A) tan 4 (B) tan 4 USE A CALCULATOR TO FIND THE VALUE OF THE TRIGONOMETRIC FUNCTION TO FOUR DECIMAL PLACES. 24. cos 10 25. cot 12 23. sin 0.8 27. Use the triangle to find each of the six trigonometric functions of . 26. 6 sec 1 5 USE RIGHT TRIANGLE RATIOS TO SOLVE THE FOLLOWING. SHOW WORK. 28. A building that is 21 meters tall casts a shadow 25 meters long. Find the angle of elevation of the sun to the nearest degree. 29. Sighting the top of a building, a surveyor measured the angle of elevation to be 22°. The transit is 300 feet from the building. Find the building’s height, to the nearest foot, if the transit if 5 feet off the ground. 30. A plane rises from take-off and flies at an angle of 10° with the horizontal runway. When it has gained an altitude of 500 feet, find the distance, to the nearest foot, the plane has flown. 31. If (-4, 3) is a point on the terminal side of angle , find the exact value of each of the six trigonometric functions of . LET BE AN ANGLE IN STANDARD POSITION. NAME THE QUADRANT IN WHICH LIES. 32. sin < 0, cos < 0 33. cot > 0, sec < 0 FIND THE REFERENCE ANGLE FOR EACH ANGLE. 34. 160° 35. -250° 36. 7 4 37. 13 3 FIND THE EXACT VALUE OF EACH EXPRESSION. DO NOT USE A CALCULATOR. USE A REFERENCE ANGLE WHEN NECESSARY. 38. cos 45° 39. sin 180° 40. cot 120° 41. sec (-30°) 42. csc (-390°) 43. tan (765°) 44. tan 4 45. cos 5 4 46. csc 47. sin 20 3 48. 2 sec 3 49. 7 cot 6