Trigonometry Practice Quiz
Take as much time as you need to complete the test. When you are finished, check your answers with the answer key that follows the test. Along with each answer is a number that tells you which lesson of this book teaches you about the trigonometry skills needed for that question. Once you know your score on the posttest, compare the results with the pretest. If you scored better on the posttest than you did on the pretest, congratulations! You have profited from your hard work. At this point, you should look at the questions you missed, if any. Do you know why you missed the question, or do you need to go back to the lesson and review the concept? If you can figure out why you missed the problem, then you understand the concept and simply need to concentrate more on accuracy when taking a test. If you missed a question because you did not know how to work the problem, go back to the lesson and spend more time working that type of problem. Take the time to understand trigonometry thoroughly. You need a solid foundation in trigonometry if you plan to use this information or progress to a higher level. Whatever your score on this posttest, keep this book for review and future reference.
Solve questions 1-29 without using a calculator.
1. | Convert the angle measure into degrees. | |
a. | 90° | |
b. | 45° | |
c. | 30° | |
d. | 60° | |
2. | Convert 120° into radians. | |
a. | 120π | |
b. | ||
c. | ||
d. | ||
3. | Which of the following could be the measure of this angle? | |
a. | 135° | |
b. | 225° | |
c. | 270° | |
d. | 315° | |
4. | If a triangle has angles of measure 24° and 68°, then what is the measure of the third angle? | |
a. | 46° | |
b. | 78° | |
c. | 88° | |
d. | 92° | |
5. | Find the length of the side marked x. | |
a. | 22 feet | |
b. | 26 feet | |
c. | 27.6 feet | |
d. | 30.7 feet | |
6. | Find the length of the side labeled x. | |
a. | √55 inches | |
b. | √73 inches | |
c. | 11 inches | |
d. | 73 inches | |
7. | Find the length of the side labeled x. | |
a. | 4√5 centimeters | |
b. | 4 √10 centimeters | |
c. | 4√13 centimeters | |
d. | 10 centimeters | |
8. | If g(x) = , what is g( –1)? | |
a. | –2 | |
b. | 2 | |
c. | ||
d. | ||
9. | What is the domain of y(x) = √4 – x? | |
a. | x < 4 | |
b. | x ≤ 4 | |
c. | x ≥ –4 | |
d. | x > –4 | |
10. | What is sin(x) for angle x in the figure? | |
a. | ||
b. | ||
c. | ||
d. | 16 | |
11. | What is sin(x) for angle x in the figure? | |
a. | ||
b. | √3 | |
c. | 5√3 | |
d. | ||
12. | Find cos(x) for the angle x in the figure. | |
a. | ||
b. | ||
c. | ||
d. | ||
13. | If sin(x) = , then what is cos(x)? | |
a. | ||
b. | ||
c. | ||
d. | ||
14. | Find tan(x) for angle x in the figure. | |
a. | ||
b. | ||
c. | ||
d. | ||
15. | If tan(x) = 2, then what is cos(x)? | |
a. | ||
b. | ||
c. | ||
d. | ||
Use the following to answer questions 16 and 17. | ||
16. | What is sec (x) for the angle x in the figure? | |
a. | ||
b. | ||
c. | ||
d. | ||
17. | What is cot(x) for the angle x in the figure? | |
a. | ||
b. | ||
c. | ||
d. | ||
18. | Which of the following is NOT true? | |
a. | cot(x) = tan(90° – x) | |
b. | ||
c. | sin^{2}(x) + cos^{2}(x) = 1 | |
d. | tan^{2}(x) + 1 = sec^{2}(x) | |
19. | Write entirely in terms of sin(x) and cos(x). | |
a. | ||
b. | ||
c. | ||
d. | ||
20. | Evaluate tan(45°). | |
a. | ||
b. | ||
c. | 1 | |
d. | √3 | |
21. | Evaluate cos. | |
a. | 0 | |
b. | ||
c. | ||
d. | ||
22. | Evaluate sec(60°). | |
a. | 2 | |
b. | ||
c. | ||
d. | ||
23. | At what point is the unit circle intersected by an angle of 210°? (Suppose that the angle is measured counterclockwise from the positive x-axis.) | |
a. | ||
b. | ||
c. | ||
d. | ||
24. | What is cos(150°)? | |
a. | ||
b. | ||
c. | ||
d. | ||
25. | What is sin? | |
a. | ||
b. | ||
c. | ||
d. | ||
26. | Evaluate tan | |
a. | 1 | |
b. | –1 | |
c. | √3 | |
d. | –√3 | |
27. | Evaluate sin^{–1} | |
a. | 30° | |
b. | 45° | |
c. | 60° | |
d. | 90° | |
28. | Evaluate cos^{–1}(0). | |
a. | 30° | |
b. | 45° | |
c. | 60° | |
d. | 90° | |
29. | What is the area of a triangle with two sides 10 inches long and one side 6 inches long? | |
a. | 25 in.^{2} | |
b. | 30 in.^{2} | |
c. | 3√7 in.^{2} | |
d. | 3√91 in.^{2} | |
Use a calculator to solve questions 30-48. |
||
30. | If a television screen is 28 inches on the diagonal and 24 inches wide, how tall is it? | |
a. | 14.4 in. | |
b. | 16.1 in. | |
c. | 27.5 in. | |
d. | 36.9 in. | |
31. | If cos(40°) = 0.766, then what is sin(50°)? | |
a. | 0.234 | |
b. | 0.6128 | |
c. | 0.766 | |
d. | 0.9575 | |
32. | Use a calculator to estimate the length x in the figure. | |
a. | 4.77 in. | |
b. | 7.51 in. | |
c. | 7.63 in. | |
d. | 10.61 in. | |
33. | Use a calculator to estimate the length x in the figure. | |
a. | 10.82 m | |
b. | 14.86 m | |
c. | 15.43 m | |
d. | 29.96 m | |
34. | Suppose a 25-foot ladder is leaned against a wall so that it makes a 70° angle with the ground. How far from the wall is the base of the ladder? | |
a. | 8.6 ft. | |
b. | 23.5 ft. | |
c. | 26.6 ft. | |
d. | 73 ft. | |
35. | A wire runs straight from the top of a 40-foot pole to the ground. If it will make a 41° angle with the ground, how long is the wire? | |
a. | 26 ft. | |
b. | 46 ft. | |
c. | 53 ft. | |
d. | 61 ft. | |
36. | Use a calculator to estimate the angle x in the figure. | |
a. | 31° | |
b. | 36.9° | |
c. | 53.1° | |
d. | 59° | |
37. | A 40-foot rope is attached to a window that is 25 feet off the ground. If the rope is pulled tight to a spot on the ground, what angle will it make with the ground? | |
a. | 32° | |
b. | 39° | |
c. | 51° | |
d. | 58° | |
38. | A ramp will run 25 feet horizontally and 5 feet vertically. At what angle will the ramp run? | |
a. | 11.3° | |
b. | 11.5° | |
c. | 12.8° | |
d. | 15.1° | |
39. | Suppose a 10-foot board leans against a tree. If the bottom of the board is 4 feet from the tree, what angle does the board make with the ground? | |
a. | 21.8° | |
b. | 23.6° | |
c. | 51.8° | |
d. | 66.4° | |
40. | Suppose a person drags a heavy weight across the ground by pulling with 100 pounds of force at a 35° angle, as illustrated in the figure. How much of the force is actually pulling the weight in the direction it is moving? | |
a. | 57 lbs. | |
b. | 65 lbs. | |
c. | 70 lbs. | |
d. | 82 Ibs. | |
41. | A ship travels 15 miles in the direction 20° west of south, then 8 miles at 15° north of west. In what direction should it head to go straight back to where it began? | |
a. | 28° north of east | |
b. | 37° north of east | |
c. | 43° north of east | |
d. | 41° east of north | |
42. | Find the length x in the figure. | |
a. | 9.6 ft. | |
b. | 11.1 ft. | |
c. | 13.2 ft. | |
d. | 20.2 ft. | |
43. | Find the length x in the figure. | |
a. | 29 m | |
b. | 31 m | |
c. | 32 m | |
d. | 35 m | |
44. | The following figure is not drawn accurately. Find the two possible measurements for angle x. | |
a. | 52.5° and 127.5° | |
b. | 54.1° and 125.9° | |
c. | 57.2° and 122.8° | |
d. | 62.5° and 117.5° | |
45. | Find the length x in the figure. | |
a. | 38 mm | |
b. | 40 mm | |
c. | 43 mm | |
d. | 47 mm | |
46. | Find the measure of angle x in the figure. | |
a. | 91.7° | |
b. | 92.4° | |
c. | 92.9° | |
d. | 93.2° | |
47. | What are the two lengths that x could be in the figure (not drawn to scale)? | |
a. | 53.2 cm or 74.5 cm | |
b. | 54.5 cm or 73.4 cm | |
c. | 56.2 cm or 71.5 cm | |
d. | 57.1 cm or 70.4 cm | |
48. | What is the approximate area of a triangle with sides of length 20 feet, 24 feet, and 25 feet? | |
a. | 223 ft.^{2} | |
b. | 238 ft.^{2} | |
c. | 240 ft.^{2} | |
d. | 247 ft.^{2} |
Answers
1. b.
2. c.
3. d.
4. c.
5. c.
6. b.
7. a.
8. c.
9. b.
10. b.
11. d.
12. c.
13. d.
14. b.
15. a.
16. a.
17. a.
18. b.
19. d.
20. c.
21. d.
22. a.
23. b.
24. d.
25. a.
26. d.
27. b.
28. d.
29. d.
30. a.
31. c.
32. c.
33. d.
34. a.
35. d.
36. b.
37. b.
38. a.
39. d.
40. d.
41. c.
42. b.
43. d.
44. a.
45. c.
46. b.
47. b.
48. a.
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