Introductory Trigonometry Practice Quiz
The quiz is 50 multiple-choice questions covering the topics in this book. While 50 questions can't cover every concept, skill, or shortcut taught in this book, your performance on the pretest will give you a good indication of your strengths and weaknesses.
If you score high on the pretest, you have a good foundation and should be able to work your way through the book quickly. If you score low on the pretest, don't despair. This book will take you through the trigonometry concepts, step by step. If you get a low score, you may need to take more than 20 minutes a day to work through a lesson. However, this is a self-paced program, so you can spend as much time on a lesson as you need. You decide when you fully comprehend the lesson and are ready to go on to the next one.
Take as much time as you need to do the pretest. When you are finished, check your answers with the answer key at the end of the pretest. 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. You will find that the level of difficulty increases as you work your way through the pretest.
Solve questions 1-29 without using a calculator.
1. | Convert the angle measure into degrees. | |
a. 30° | ||
b. 60° | ||
c. 180° | ||
d. 45° | ||
2. | Convert 135° into radians. | |
a. | ||
b. 135π | ||
c. | ||
d. | ||
3. | Which of the following could be the measure of this angle? | |
a. 120° | ||
b. 150° | ||
c. 240° | ||
d. 300° | ||
4. | If a triangle has angles of measure 53° and 71°, then what is the measure of the third angle? | |
a. 56° | ||
b. 62° | ||
c. 66° | ||
d. 124° | ||
5. | Find the length of the side marked x. | |
a. 8 in. | ||
b. 9 in. | ||
c. 10 in. | ||
d. 13 in. | ||
6. | Find the length of the side labeled x. | |
a. 3 ft. | ||
b. √51 ft. | ||
c. √61 ft. | ||
d. √149 ft. | ||
7. | Find the length of the side labeled x. | |
a. 8 cm | ||
b. 2√5 cm | ||
c. √10 cm | ||
d. 2√13 cm | ||
8. | If f(x) = 4x^{2} – 7x + 2, what is f (–2)? | |
a. 4 | ||
b. 32 | ||
c. 4x^{2} – 7x | ||
d. –8x^{2} + 14x – 4 | ||
9. | What is the domain of h(x) = √x+5? | |
a. x ≥ – 5 | ||
b. x < – 5 | ||
c. x ≥ 5 | ||
d. x > 5 | ||
10. | What is sin(x) for the angle x in the figure? | |
a. | ||
b. | ||
c. √119 | ||
d. | ||
11. | What is sin(x) for the angle x in the figure? | |
a. | ||
b. √15 | ||
c. | ||
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) = 3, then what is sin(x)? | |
a. 3 | ||
b. | ||
c. | ||
d. |
Use the following figure 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. sin^{2}(x) + cos^{2}(x) = 1 | |
b. | |
c. sec(x) = csc(90° – x) | |
d. csc^{2}(x) + 1 = cot^{2}(x) | |
19. | Write entirely in terms of sin(x) and cos(x). |
a. | |
b. | |
c. | |
d. | |
20. | Evaluate tan(60°). |
a. | |
b. √3 | |
c. | |
d. 1 | |
21. | Evaluate sin . |
a. | |
b. | |
c. | |
d. 1 | |
22. | Evaluate sec(30°). |
a. 2 | |
b. | |
c. | |
d. | |
23. | At what point is the unit circle intersected by an angle of 315°? (Suppose that the angle is measured counterclockwise from the positive x-axis.) |
a. | |
b. | |
c. | |
d. | |
24. | What is sin(240° )? |
a. | |
b. | |
c. | |
d. | |
25. | What is cos |
a. | |
b. | |
c. | |
d. | |
26. | Evaluate tan. |
a. 1 | |
b. –1 | |
c. √3 | |
d. –√3 | |
27. | Evaluate cos^{–1}. |
a. 30° | |
b. 45° | |
c. 60° | |
d. 90° | |
28. | Evaluate sin^{–1}(1). |
a. 30° | |
b. 45° | |
c. 60° | |
d. 90° | |
29. | What is the area of an equilateral triangle with all sides of length 8 inches? |
a. 24 in.^{2} | |
b. 32 in.^{2} | |
c. 16√2in.^{2} | |
d. 16√3 in.^{2} |
Use a calculator to solve questions 30–50.
30. | Suppose a 20-foot ladder is leaned against a wall from 6 feet away. Approximately how high up will it reach? |
a. 14 ft. | |
b. 18 ft. | |
c. 19.1 ft. | |
d. 20.9 ft. | |
31. | If sin(65°) = 0.9063, then what is cos(25°)? |
a. .0937 | |
b. 0.3486 | |
c. 0.4244 | |
d. 0.9063 | |
32. | Estimate the length x in the figure. |
a. 0.057 in. | |
b. 3.63 in. | |
c. 7.13 in. | |
d. 7.65 in. | |
33. | Estimate the length x in the figure. |
a. 2.28 m | |
b.16.34 m | |
c. 12.34 m | |
d. 88.39 m | |
34. | A wire will be attached straight from the top of a 20-foot pole to the ground. If it needs to make a 60° angle with the ground, how long must the wire be? |
a. 10 ft. | |
b.17.3 ft. | |
c. 23.1 ft. | |
d. 40 ft. | |
35. | A person at the top of a 50-foot-tall tower sees a car at 10° below the horizontal. How far is the car from the base of the tower? |
a. 9 ft. | |
b.51 ft. | |
c. 284 ft. | |
d. 288 ft. | |
36. | Estimate the angle x in the figure. |
a. 29.7° | |
b. 34.8° | |
c. 55.2° | |
d. 60.3° | |
37. | A 35-foot board leans against a wall. If the top of the board is 32 feet up the wall, what angle does the board make with the floor? |
a. 24° | |
b. 42° | |
c. 66° | |
d. 85° | |
38. | A ship's destination is 30 miles north and 12 miles east. At what angle should it head to go straight to its destination? |
a. 22°east of north | |
b. 24°east of north | |
c. 31°east of north | |
d. 66°east of north | |
39. | Suppose a mountain road descends 2,000 feet over the course of 4 miles. If the slope of the road were constant, at what angle would it descend? |
a. 5.4° | |
b. 6.1° | |
c. 9.3° | |
d. 10.1° | |
40. | Suppose a person drags a heavy weight across the ground by pulling with 75 pounds of force at a 25° angle, as illustrated in the figure. How much of the force is actually pulling the weight in the direction it is moving? |
a. 32 Ibs. | |
b. 35 Ibs. | |
c. 50 Ibs. | |
d. 68 Ibs. | |
41. | A group of hikers travels 2,000 meters in the direction that is 30° east of north. They then go 1,700 meters in the direction 40° north of west. At this point, in what direction would they head to go straight back to where they started? |
a. 5.7° east of south | |
b. 6.1° east of south | |
c. 12° east of south | |
d. 14.2° east of south | |
42. | Find the length x in the figure. |
a. 13.9 m | |
b. 15.7 m | |
c. 16.2 m | |
d. 25.4 m | |
43. | Find the length x in the figure. |
a. 100 ft. | |
b. 103 ft. | |
c. 154 ft. | |
d. 169 ft. | |
44. | The following figure is not drawn accurately. Find the two possible measurements for angle x. |
a. 50° and 130° | |
b. 53° and 127° | |
c. 55° and 125° | |
d. 57°and 123° | |
45. | Find the length x in the figure. |
a. 18.5 ft. | |
b. 19.7 ft. | |
c. 20.3 ft. | |
d. 20.9 ft. | |
46. | Find the measure of angle x in the figure. |
a. 32.1° | |
b. 36.3° | |
c. 37.5° | |
d. 41.8° | |
47. | What are the two lengths that x could be in the figure (not drawn to scale)? |
a. 8 in. or 22 in. | |
b. 9 in. or 21 in. | |
c. 10 in. or 20 in. | |
d. 13 in. or 17 in. | |
48. | What is the area of a triangle with lengths 5 inches, 6 inches, and 7 inches? |
a. 15 in.^{2} | |
b. 2√6in.^{2} | |
c. 4√6in.^{2} | |
d. 6√6in.^{2} | |
49. | A family drives down a straight stretch of highway for 25 miles. When they begin driving, a distant mountain can be seen 30° off to the right of the road. When they finish driving, the mountain now appears to be 70° to the right of the road. How far away is the mountain from them when they have finished driving? |
a. 17 mi. | |
b. 19 mi. | |
c. 21 mi. | |
d. 23 mi. | |
50. | A 20-foot-tall inflatable dog has been installed on top of a restaurant. The angle to the top of the dog is 72° from where a person on the ground is standing. The angle to the bottom of the dog is 61°. How far away is the restaurant from where the person is standing? |
a. 15 ft. | |
b. 20 ft. | |
c. 25 ft. | |
d. 30 ft. |
Answers
1. a.
2. d.
3. c.
4. a.
5. b.
6. b.
7. d.
8. b.
9. a.
10. a.
11. d.
12. c.
13. d.
14. a.
15. c.
16. b.
17. c.
18. d.
19. a.
20. b.
21. b.
22. d.
23. a.
24. d.
25. b.
26. b.
27. a.
28. d.
29. d.
30. c.
31. d.
32. b.
33. b.
34. c.
35. c.
36. a.
37. c.
38. a.
39. a.
40. d.
41. b.
42. b.
43. d.
44. a.
45. b.
46. b.
47. c.
48. d.
49. b.
50. a.
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