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Free Practice Quiz Question List

05 Trigonometric Functions Online Quiz Questions

Use this free practice quiz with 20 questions to review 05 Trigonometric Functions, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose one
1 point

Which radian measure is equivalent to 60∘60^\circ?

  1. A

    π6\frac{\pi}{6}

  2. B

    π3\frac{\pi}{3}

  3. C

    2π3\frac{2\pi}{3}

  4. D

    3π3\pi

02
Choose all
1 point

Select all statements that are true when tt lies in Quadrant II.

  1. A

    cos⁡t<0\cos t<0

  2. B

    sin⁡t<0\sin t<0

  3. C

    tan⁡t>0\tan t>0

  4. D

    tan⁡t<0\tan t<0

03
True or false
1 point

True or false: On the unit circle, the terminal point for an angle tt has coordinates (cos⁡t,sin⁡t)(\cos t,\sin t).

  1. A

    True

  2. B

    False

04
Written response
1 point

What is the exact value of sin⁡(π3)\sin\left(\frac{\pi}{3}\right)?

05
Fill in the blank
1 point

The period of the function y=sin⁡xy=\sin x is .

06
Choose one
1 point

What is the amplitude of y=3sin⁡(2x−π2)+1y=3\sin\left(2x-\frac{\pi}{2}\right)+1?

  1. A

    11

  2. B

    22

  3. C

    33

  4. D

    66

07
Choose all
1 point

Select all correct reciprocal identities.

  1. A

    sec⁡x=1sin⁡x\sec x=\frac{1}{\sin x}

  2. B

    sec⁡x=1cos⁡x\sec x=\frac{1}{\cos x}

  3. C

    csc⁡x=1sin⁡x\csc x=\frac{1}{\sin x}

  4. D

    csc⁡x=1cos⁡x\csc x=\frac{1}{\cos x}

08
True or false
1 point

True or false: The identity 1+tan⁡2x=sec⁡2x1+\tan^2x=\sec^2x follows by dividing sin⁡2x+cos⁡2x=1\sin^2x+\cos^2x=1 by cos⁡2x\cos^2x, where defined.

  1. A

    True

  2. B

    False

09
Written response
1 point

Evaluate arctan⁡(1)\arctan(1) exactly in radians.

10
Fill in the blank
1 point

For 0≤x<2π0\le x<2\pi, the solutions to sin⁡x=12\sin x=\frac{1}{2} are x=π6x=\frac{\pi}{6} and .

11
Choose one
1 point

What is the period of y=3sin⁡(2x−π2)+1y=3\sin\left(2x-\frac{\pi}{2}\right)+1?

  1. A

    π\pi

  2. B

    2π2\pi

  3. C

    π2\frac{\pi}{2}

  4. D

    4π4\pi

12
Open ended
1 point

Show algebraically, using a fundamental identity and the quotient and reciprocal identities, why 1+tan⁡2x=sec⁡2x1+\tan^2x=\sec^2x wherever the expressions are defined.

13
Choose one
1 point

What is the principal value of arccos⁡(−1)\arccos(-1)?

  1. A

    −π-\pi

  2. B

    00

  3. C

    π\pi

  4. D

    2π2\pi

14
Choose one
1 point

What is 150∘150^\circ expressed in radians?

  1. A

    2π3\frac{2\pi}{3}

  2. B

    3π4\frac{3\pi}{4}

  3. C

    5π6\frac{5\pi}{6}

  4. D

    7π6\frac{7\pi}{6}

15
Choose one
1 point

Which point on the unit circle corresponds to the angle 5π3\frac{5\pi}{3}?

  1. A

    (−12,32)\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)

  2. B

    (12,−32)\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)

  3. C

    (−12,−32)\left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right)

  4. D

    (32,−12)\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)

16
True or false
1 point

True or false: The tangent function has period π\pi.

  1. A

    True

  2. B

    False

17
Choose one
1 point

For y=−2cos⁡(3(x−π6))+4y=-2\cos\left(3\left(x-\frac{\pi}{6}\right)\right)+4, which set of features is correct?

  1. A

    Amplitude 22, period 2π3\frac{2\pi}{3}, shift π6\frac{\pi}{6} right, and midline y=4y=4

  2. B

    Amplitude 22, period 3π3\pi, shift π6\frac{\pi}{6} left, and midline y=−4y=-4

  3. C

    Amplitude −2-2, period 2π3\frac{2\pi}{3}, shift π3\frac{\pi}{3} right, and midline y=4y=4

  4. D

    Amplitude 44, period 2π3\frac{2\pi}{3}, shift π6\frac{\pi}{6} right, and midline y=2y=2

18
Written response
1 point

Evaluate arccos⁡(−1)\arccos(-1). Give the exact principal angle in radians.

19
Choose one
1 point

If tan⁡x=34\tan x=\frac{3}{4} and xx lies in Quadrant I, what is sec⁡x\sec x?

  1. A

    34\frac{3}{4}

  2. B

    45\frac{4}{5}

  3. C

    54\frac{5}{4}

  4. D

    74\frac{7}{4}

20
Written response
1 point

Solve sin⁡x=−32\sin x=-\frac{\sqrt{3}}{2} for 0≤x<2π0\le x<2\pi. Enter both solutions in increasing order.