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Free Practice Quiz Question List

Trigonometric Foundations Online Quiz Questions

Use this free practice quiz with 20 questions to review Trigonometric Foundations, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose one
1 point

Convert 150∘150^\circ to radians.

  1. A

    3π4\frac{3\pi}{4}

  2. B

    2π3\frac{2\pi}{3}

  3. C

    5π6\frac{5\pi}{6}

  4. D

    7π6\frac{7\pi}{6}

02
True or false
1 point

In standard position, a positive angle is generated by a counterclockwise rotation.

  1. A

    True

  2. B

    False

03
Choose one
1 point

Which point on the unit circle corresponds to θ=2π3\theta=\frac{2\pi}{3}?

  1. A

    (12,32)\left(\frac12,\frac{\sqrt3}{2}\right)

  2. B

    (−12,32)\left(-\frac12,\frac{\sqrt3}{2}\right)

  3. C

    (−32,12)\left(-\frac{\sqrt3}{2},\frac12\right)

  4. D

    (32,−12)\left(\frac{\sqrt3}{2},-\frac12\right)

04
Written response
1 point

What term describes two angles that have the same initial and terminal sides?

05
Choose all
1 point

Select all statements that are true when θ\theta lies in Quadrant II.

  1. A

    cos⁡θ<0\cos\theta<0

  2. B

    sin⁡θ<0\sin\theta<0

  3. C

    tan⁡θ<0\tan\theta<0

  4. D

    sin⁡θ>0\sin\theta>0

06
Fill in the blank
1 point

Complete both statements: For a circle of radius rr intercepting an arc of length ss, the radian measure is θ=\theta=. For a unit circle, the radius is .

07
True or false
1 point

The statement “Tangent is undefined whenever cos⁡θ=0\cos\theta=0” is:

  1. A

    True

  2. B

    False

08
Choose one
1 point

Evaluate tan⁡(11π6)\tan\left(\frac{11\pi}{6}\right).

  1. A

    33\frac{\sqrt3}{3}

  2. B

    −3-\sqrt3

  3. C

    3\sqrt3

  4. D

    −33-\frac{\sqrt3}{3}

09
Written response
1 point

What is the value of sin⁡(5π6)\sin\left(\frac{5\pi}{6}\right)? Enter the exact value as a decimal or fraction; no tolerance is allowed.

10
Choose all
1 point

Select all equations that are trigonometric identities stated in the material.

  1. A

    tan⁡θ=sin⁡θcos⁡θ\tan\theta=\frac{\sin\theta}{\cos\theta}

  2. B

    sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1

  3. C

    sin⁡θ+cos⁡θ=1\sin\theta+\cos\theta=1

  4. D

    sin⁡(−θ)=−sin⁡θ\sin(-\theta)=-\sin\theta

11
Fill in the blank
1 point

Complete the reciprocal identities: csc⁡θ=\csc\theta= and sec⁡θ=\sec\theta=.

12
Choose one
1 point

What is the reference angle for θ=7π4\theta=\frac{7\pi}{4}?

  1. A

    3π4\frac{3\pi}{4}

  2. B

    π4\frac\pi4

  3. C

    5π4\frac{5\pi}{4}

  4. D

    7π4\frac{7\pi}{4}

13
Open ended
1 point

Given that sin⁡θ=35\sin\theta=\frac35 and θ\theta lies in Quadrant II, find cos⁡θ\cos\theta. Show how the Pythagorean identity and the quadrant determine your answer.

14
Choose one
1 point

Evaluate sin⁡(π2−π6)\sin\left(\frac\pi2-\frac\pi6\right) using a cofunction identity.

  1. A

    12\frac12

  2. B

    32\frac{\sqrt3}{2}

  3. C

    11

  4. D

    22\frac{\sqrt2}{2}

15
True or false
1 point

True or false: tan⁡θ\tan\theta is undefined whenever cos⁡θ=0\cos\theta=0.

  1. A

    True

  2. B

    False

16
Choose one
1 point

What point on the unit circle corresponds to the angle 7π4\frac{7\pi}{4}?

  1. A

    (−22,22)\left(-\frac{\sqrt2}{2},\frac{\sqrt2}{2}\right)

  2. B

    (22,22)\left(\frac{\sqrt2}{2},\frac{\sqrt2}{2}\right)

  3. C

    (22,−22)\left(\frac{\sqrt2}{2},-\frac{\sqrt2}{2}\right)

  4. D

    (−22,−22)\left(-\frac{\sqrt2}{2},-\frac{\sqrt2}{2}\right)

17
Written response
1 point

What coterminal angle results from adding exactly one complete revolution, 2π2\pi, to π3\frac{\pi}{3}? Express your answer exactly in radians.

18
Written response
1 point

Which trigonometric function equals 1cos⁡θ\frac{1}{\cos\theta}? Enter its standard notation.

19
Choose one
1 point

If sin⁡θ=35\sin\theta=\frac35 and θ\theta lies in Quadrant II, what is cos⁡θ\cos\theta?

  1. A

    45\frac45

  2. B

    −35-\frac35

  3. C

    −45-\frac45

  4. D

    35\frac35

20
Choose one
1 point

What is the reference angle for 13π6\frac{13\pi}{6}?

  1. A

    π3\frac{\pi}{3}

  2. B

    π6\frac{\pi}{6}

  3. C

    5π6\frac{5\pi}{6}

  4. D

    11π6\frac{11\pi}{6}