Training Trigonometry Placement Test Practice — Trigonometry
5 / 5

Placement Test Practice — Trigonometry

25 min Trigonometry

Placement Test Practice — Trigonometry

This practice test covers the full range of trigonometry topics from this module — angle measurement, right triangles, the unit circle, and trigonometric identities. Use it to consolidate your learning and identify any gaps before moving on.

The problems range from straightforward conversions and triangle calculations to identity proofs and applied problems, giving you a comprehensive review.

These problems cover the range of trigonometry topics seen on college placement exams.

Practice Test — 25 Questions

1. Convert $240°$ to radians.
2. Convert $\dfrac{5\pi}{6}$ to degrees.
3. Find the exact value of $\sin 45°$.
4. Find the exact value of $\cos \dfrac{\pi}{3}$.
5. Find the exact value of $\tan 150°$.
6. If a right triangle has opposite = 7 and adjacent = 24, find $\sin\theta$.
7. Find the reference angle for $320°$.
8. In which quadrant is $\sin\theta < 0$ and $\cos\theta > 0$?
9. Evaluate $\sin^2 45° + \cos^2 45°$.
10. Simplify $\tan\theta \cdot \cos\theta$.
11. Find arc length: $r = 6$, $\theta = \dfrac{\pi}{3}$.
12. If $\cos\theta = \dfrac{3}{5}$ (QI), find $\tan\theta$.
13. Find $\cos 330°$.
14. Find $\sin \dfrac{5\pi}{4}$.
15. Simplify $\dfrac{\sin\theta}{\cos\theta}$.
16. Find $\sec 60°$.
17. If $\tan\theta = -1$ and $\theta$ is in QII, find $\theta$.
18. Evaluate $2\sin 30° \cos 30°$.
19. Find the area of a sector: $r = 10$, $\theta = 72°$.
20. From a point 80 ft from a building, the angle of elevation is $62°$. Find the height.
21. Find $\cot\dfrac{\pi}{4}$.
22. Simplify $1 + \tan^2\theta$.
23. Find $\cos(-60°)$.
24. If $\sin\theta = -\dfrac{\sqrt{3}}{2}$ and $\cos\theta = \dfrac{1}{2}$, find $\theta$ in $[0°, 360°)$.
25. A Ferris wheel with radius 30 m rotates $\frac{2\pi}{3}$ radians. How far does a rider travel?
Show Answer Key

1. $\dfrac{4\pi}{3}$

2. $150°$

3. $\dfrac{\sqrt{2}}{2}$

4. $\dfrac{1}{2}$

5. $-\dfrac{\sqrt{3}}{3}$

6. hyp $= 25$; $\sin\theta = \frac{7}{25}$

7. $360° - 320° = 40°$

8. Quadrant IV

9. $1$

10. $\sin\theta$

11. $s = 6 \cdot \frac{\pi}{3} = 2\pi \approx 6.28$

12. $\sin\theta = \frac{4}{5}$; $\tan\theta = \frac{4}{3}$

13. $\dfrac{\sqrt{3}}{2}$

14. $-\dfrac{\sqrt{2}}{2}$

15. $\tan\theta$

16. $2$

17. $\theta = 135°$

18. $2 \cdot \frac{1}{2} \cdot \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{2}$ (this is $\sin 60°$)

19. $72° = \frac{2\pi}{5}$; $A = \frac{1}{2}(100)\frac{2\pi}{5} = 20\pi \approx 62.83$ sq units

20. $h = 80\tan 62° \approx 150.5$ ft

21. $1$

22. $\sec^2\theta$

23. $\frac{1}{2}$ (cosine is even)

24. $300°$ (QIV)

25. $s = 30 \cdot \frac{2\pi}{3} = 20\pi \approx 62.83$ m

Trigonometric Identities Back to Module