PreCalc: Chapter 6 Test Review
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1 Name: Class: Date: ID: A PreCalc: Chapter 6 Test Review Short Answer 1. Draw the angle Draw the angle. 3. Convert the angle to a decimal in degrees. Round the answer to two decimal places. 8. If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. Round to one decimal place, if necessary. r = feet, s = 5 feet, θ =? 9. Find the length s. Round the answer to three decimal places '35'' 4. Convert the angle to a decimal in degrees. Round the answer to two decimal places '48'' 5. Convert the angle to D M' S'' form. Round the answer to the nearest second Find the length s. Round the answer to three decimal places. 6. Convert the angle to D M' S'' form. Round the answer to the nearest second If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. Round to one decimal place, if necessary. r = 14.8 inches, θ = 315, s =? 11. Convert the angle in degrees to radians. Express the answer as multiple of π. 54 1
2 Name: ID: A 12. Convert the angle in radians to degrees. 13. If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. θ = radians, A = 62 square meters, r =? 14. If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. r = 5 feet, A = 33 square feet, θ =? 15. Solve the problem. As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 110 square yards in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places. 16. Solve the problem. The blade of a windshield wiper sweeps out an angle of 135 in one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle? (Round to the nearest 0.1 square inch.) 17. In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. (, ) Find tan t. 18. In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. (, ) Find sec t. 19. Find the exact value. Do not use a calculator. sin 2π 20. Find the exact value. Do not use a calculator. cot Find the exact value of the expression. Do not use a calculator. sec 60 sin Find the exact value of the expression. Do not use a calculator. tan cos 23. Find the exact value. Do not use a calculator. cos 24. Find the exact value. Do not use a calculator. sin Find the exact value of the expression. Do not use a calculator. cos + tan 26. Find the exact value of the expression. Do not use a calculator. tan 150 cos 210 2
3 Name: ID: A 27. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. (, ) Find cos θ. 34. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. sin θ =, cos θ = Find csc θ. 28. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. (3, 2) Find tan θ. 29. Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. tan Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. sec 31. Name the quadrant in which the angle θ lies. 35. Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. sec 2 35 tan Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator. sin 20 csc Find the exact value of the indicated trigonometric function of θ. tan θ =, θ in quadrant II Find cos θ. 38. Find the exact value of the indicated trigonometric function of θ. csc θ =, θ in quadrant III Find cot θ. 32. Name the quadrant in which the angle θ lies. 33. In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function. sin θ =, cos θ = Find cot θ. 39. Find the exact value of the indicated trigonometric function of θ. sin θ =, tan θ > 0 Find sec θ. 40. Find the exact value of the indicated trigonometric function of θ. cot θ =, cos θ < 0 Find csc θ. 3
4 Name: ID: A 41. Use the evenodd properties to find the exact value of the expression. Do not use a calculator. sin (60 ) 46. Use transformations to graph the function. y = 3 sin(3x) 42. Use the evenodd properties to find the exact value of the expression. Do not use a calculator. csc (60 ) 43. Use the evenodd properties to find the exact value of the expression. Do not use a calculator. csc 44. Use the evenodd properties to find the exact value of the expression. Do not use a calculator. 47. Use transformations to graph the function. y = 3 sin cot 45. Use transformations to graph the function. y = 4 sin x 4
5 Name: ID: A 48. Use transformations to graph the function. y = 5 cos x 52. Write the equation of a sine function that has the given characteristics. Amplitude: 3 Period: Graph the function. y = 3 tan(2x) 49. Use transformations to graph the function. y = 3 cos(3x) 54. Graph the function. y = 3 tan 50. Without graphing the function, determine its amplitude or period as requested. y = sin Find the period. 51. Without graphing the function, determine its amplitude or period as requested. y = cos Find the amplitude. 5
6 Name: ID: A 55. Graph the function. y = cot(πx) 57. Graph the function. y = sec(2x) 56. Graph the function. y = 3 cot(2x) 58. Graph the function. y = 2 csc 6
7 PreCalc: Chapter 6 Test Review Answer Section SHORT ANSWER 1. ANS: 2. ANS: 3. ANS: ANS: ANS: 14 55'48'' 6. ANS: 217 1'48'' 7. ANS: 81.4 in. 1
8 8. ANS: 15 radians 9. ANS: yd 10. ANS: m 11. ANS: 12. ANS: ANS: m 14. ANS: ANS: ANS: in ANS: 18. ANS: 2
9 19. ANS: ANS: undefined 21. ANS: 22. ANS: 23. ANS: 24. ANS: 25. ANS: 26. ANS: 27. ANS: 3
10 28. ANS: 29. ANS: 30. ANS: 31. ANS: III 32. ANS: III 33. ANS: 34. ANS: 35. ANS: ANS: ANS: 4
11 38. ANS: 39. ANS: 40. ANS: 41. ANS: 42. ANS: ANS: 44. ANS: 5
12 45. ANS: 46. ANS: 47. ANS: 6
13 48. ANS: 49. ANS: 50. ANS: 51. ANS: 52. ANS: y = 3 sin 7
14 53. ANS: 54. ANS: 8
15 55. ANS: 56. ANS: 9
16 57. ANS: 58. ANS: 10
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