Back to teacher guide Browse all worksheets
Show answer keyShare to Classroom

Assign this topic online, free

A 10-question class quiz: students answer on their phones with instant feedback, you see every score live. No student accounts.

Students who get stuck can practice with step-by-step help: open the interactive lesson

Mathorio

Worksheet

Quotient Identities

Name:
Class:
Date:

Show your work for each problem.

  1. 1.
    Which expression is equal to tan⁡θ\tan\theta?
    1. a)sin⁡θcos⁡θ\frac{\sin\theta}{\cos\theta}
    2. b)sin⁡θcos⁡θ\sin\theta\cos\theta
    3. c)1sin⁡θ\frac{1}{\sin\theta}
    4. d)cos⁡θsin⁡θ\frac{\cos\theta}{\sin\theta}
  2. 2.
    Which expression is equal to cot⁡θ\cot\theta?
    1. a)sin⁡θcos⁡θ\frac{\sin\theta}{\cos\theta}
    2. b)sin⁡θcos⁡θ\sin\theta\cos\theta
    3. c)cos⁡θsin⁡θ\frac{\cos\theta}{\sin\theta}
    4. d)1cos⁡θ\frac{1}{\cos\theta}
  3. 3.
    For an angle θ\theta, sin⁡θ=0.6\sin\theta = 0.6 and cos⁡θ=0.8\cos\theta = 0.8. What is tan⁡θ\tan\theta?
  4. 4.
    For an angle θ\theta, sin⁡θ=513\sin\theta = \frac{5}{13} and cos⁡θ=1213\cos\theta = \frac{12}{13}. What is cot⁡θ\cot\theta? Give a fraction.
  5. 5.
    For an angle θ\theta, sin⁡θ=817\sin\theta = \frac{8}{17} and cos⁡θ=1517\cos\theta = \frac{15}{17}. Find tan⁡θ\tan\theta and cot⁡θ\cot\theta.
  6. 6.
    For which angle is tan⁡θ\tan\theta undefined?
    1. a)0°0°
    2. b)180°180°
    3. c)90°90°
    4. d)45°45°
  7. 7.
    Without a calculator: what is tan⁡37°⋅cot⁡37°\tan 37° \cdot \cot 37°?
  8. 8.
    Simplify sin⁡θcot⁡θ\sin\theta \cot\theta, then evaluate it at θ=60°\theta = 60°.
  9. 9.
    Simplify cot⁡θcos⁡θ\frac{\cot\theta}{\cos\theta}.
    1. a)sec⁡θ\sec\theta
    2. b)tan⁡θ\tan\theta
    3. c)sin⁡θ\sin\theta
    4. d)csc⁡θ\csc\theta
  10. 10.
    For an angle θ\theta, sin⁡θ=−0.8\sin\theta = -0.8 and cos⁡θ=0.6\cos\theta = 0.6. What is tan⁡θ\tan\theta? Give a fraction.
  11. 11.
    Use sin⁡30°=12\sin 30° = \frac{1}{2} and cos⁡30°=32\cos 30° = \frac{\sqrt{3}}{2} to find the exact values of tan⁡30°\tan 30° and cot⁡30°\cot 30°.
  12. 12.
    Simplify tan⁡θcsc⁡θ\tan\theta \csc\theta, then evaluate it at θ=60°\theta = 60°.
  13. 13.
    For 0°≤θ<360°0° \le \theta < 360°, at how many angles is cot⁡θ\cot\theta undefined?
  14. 14.
    The angle θ\theta lies in quadrant II and sin⁡θ=35\sin\theta = \frac{3}{5}. What is tan⁡θ\tan\theta?
    1. a)−43-\frac{4}{3}
    2. b)43\frac{4}{3}
    3. c)34\frac{3}{4}
    4. d)−34-\frac{3}{4}
  15. 15.
    The angle θ\theta lies in quadrant IV and cos⁡θ=513\cos\theta = \frac{5}{13}. Find tan⁡θ\tan\theta and cot⁡θ\cot\theta.
  16. 16.
    The angle θ\theta lies in quadrant III and cos⁡θ=−0.28\cos\theta = -0.28. What is cot⁡θ\cot\theta? Give a fraction.
  17. 17.
    Simplify sin⁡θtan⁡θ+cos⁡θcot⁡θ\frac{\sin\theta}{\tan\theta} + \frac{\cos\theta}{\cot\theta}, then evaluate it for sin⁡θ=0.6\sin\theta = 0.6 and cos⁡θ=0.8\cos\theta = 0.8.
  18. 18.
    An acute angle θ\theta satisfies 3sin⁡θ=4cos⁡θ3\sin\theta = 4\cos\theta. Find tan⁡θ\tan\theta, cot⁡θ\cot\theta, cos⁡θ\cos\theta and sin⁡θ\sin\theta.
Interactive lesson with step-by-step solutions and more practice (free): mathorio.com/en/learn/trigonometry/identities/quotient-identities
Today's challengeOne problem, three tries