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Free Practice Quiz Question List

Trigonometric Functions and Graphs Online Quiz Questions

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

20 questions
01
Choose one
1 point

What is the period of y=4sin⁡(3(x−π5))−2y=4\sin\left(3\left(x-\frac{\pi}{5}\right)\right)-2?

  1. A

    6π6\pi

  2. B

    2π3\frac{2\pi}{3}

  3. C

    3π2\frac{3\pi}{2}

  4. D

    2π2\pi

02
Choose one
1 point

What is the range of y=−2cos⁡(π3x)+1y=-2\cos\left(\frac{\pi}{3}x\right)+1?

  1. A

    [−3,1][-3,1]

  2. B

    [−2,2][-2,2]

  3. C

    [−1,3][-1,3]

  4. D

    [1,5][1,5]

03
Choose one
1 point

For g(x)=−2tan⁡(2(x−π4))+1g(x)=-2\tan\left(2\left(x-\frac{\pi}{4}\right)\right)+1, which pair gives the two vertical asymptotes that surround the center point at x=π4x=\frac{\pi}{4}?

  1. A

    x=0x=0 and x=π2x=\frac{\pi}{2}

  2. B

    x=π4x=\frac{\pi}{4} and x=3π4x=\frac{3\pi}{4}

  3. C

    x=−π4x=-\frac{\pi}{4} and x=3π4x=\frac{3\pi}{4}

  4. D

    x=−π2x=-\frac{\pi}{2} and x=π2x=\frac{\pi}{2}

04
Choose all
1 point

Select all statements that are correct about reciprocal trigonometric functions.

  1. A

    The secant graph is the reciprocal of the cosine graph.

  2. B

    The cosecant graph has vertical asymptotes at x=kπx=k\pi.

  3. C

    The cotangent function has period 2π2\pi.

  4. D

    The cotangent function has vertical asymptotes at x=kπx=k\pi.

05
Choose all
1 point

A temperature varies between 10∘C10^\circ\text{C} and 26∘C26^\circ\text{C} during a regular 24-hour cycle. Select all correct features of a sinusoidal model for this data.

  1. A

    The amplitude is 8.

  2. B

    The midline is y=18y=18.

  3. C

    The period is 24 hours.

  4. D

    The coefficient BB must be π24\frac{\pi}{24}.

06
True or false
1 point

True or false: A transformed tangent function has no amplitude because its range is unbounded.

  1. A

    True

  2. B

    False

07
True or false
1 point

True or false: The vertical asymptotes of y=sec⁡xy=\sec x occur where cos⁡x=0\cos x=0.

  1. A

    True

  2. B

    False

08
Written response
1 point

What is the horizontal phase shift of y=5sin⁡(2(x−3))+1y=5\sin(2(x-3))+1? Give the number of units to the right.

09
Written response
1 point

What is the midline y-value of y=−4cos⁡(π2(x+1))+7y=-4\cos\left(\frac{\pi}{2}(x+1)\right)+7?

10
Fill in the blank
1 point

For f(x)=3cos⁡(π4(x−2))+5f(x)=3\cos\left(\frac{\pi}{4}(x-2)\right)+5, enter the amplitude as and the period as .

11
Fill in the blank
1 point

The function csc⁡x\csc x is the reciprocal of the function, and its vertical asymptotes occur at .

12
Open ended
1 point

Describe how to graph y=2sec⁡(x−π32)+1y=2\sec\left(\frac{x-\frac{\pi}{3}}{2}\right)+1 over one cycle. State the period, phase shift, midline, vertical asymptotes, range, and the key steps for constructing the branches.

13
Choose one
1 point

A sinusoidal model has a period of 12 time units. Which value of BB can be used in y=Asin⁡(B(t−h))+Dy=A\sin(B(t-h))+D to produce that period?

  1. A

    π12\frac{\pi}{12}

  2. B

    π4\frac{\pi}{4}

  3. C

    π6\frac{\pi}{6}

  4. D

    π3\frac{\pi}{3}

14
Choose one
1 point

What is the period of f(x)=3cos⁡(π4(x−2))+5f(x)=3\cos\left(\frac{\pi}{4}(x-2)\right)+5?

  1. A

    2 units

  2. B

    8 units

  3. C

    π/4\pi/4 units

  4. D

    4π4\pi units

15
Choose one
1 point

For g(x)=−2tan⁡(2(x−π4))+1g(x)=-2\tan\left(2\left(x-\frac{\pi}{4}\right)\right)+1, which pair gives the nearest vertical asymptotes surrounding the center point?

  1. A

    x=−π4x=-\frac{\pi}{4} and x=3π4x=\frac{3\pi}{4}

  2. B

    x=π4x=\frac{\pi}{4} and x=3π4x=\frac{3\pi}{4}

  3. C

    x=0x=0 and x=π2x=\frac{\pi}{2}

  4. D

    x=−π2x=-\frac{\pi}{2} and x=π2x=\frac{\pi}{2}

16
Choose one
1 point

The function y=sec⁡xy=\sec x is the reciprocal of cosine. Where do its vertical asymptotes occur?

  1. A

    x=π2+kπx=\frac{\pi}{2}+k\pi

  2. B

    x=kπx=k\pi

  3. C

    x=2kπx=2k\pi

  4. D

    x=π4+kπx=\frac{\pi}{4}+k\pi

17
Choose one
1 point

A temperature varies between 10∘C10^\circ\mathrm{C} and 26∘C26^\circ\mathrm{C}. Which pair gives the amplitude and midline of a sinusoidal model?

  1. A

    Amplitude 16 and midline 18

  2. B

    Amplitude 8 and midline 16

  3. C

    Amplitude 18 and midline 8

  4. D

    Amplitude 8 and midline 18

18
Written response
1 point

For y=2sin⁡(π4(x+3))−1y=2\sin\left(\frac{\pi}{4}(x+3)\right)-1, enter the period in units.

19
Written response
1 point

What is the mathematical term for the horizontal line y=Dy=D in a transformed sine or cosine function?

20
True or false
1 point

True or false: On every interval between consecutive vertical asymptotes, the graph of y=−2tan⁡(3(x−1))+5y=-2\tan\bigl(3(x-1)\bigr)+5 decreases from left to right.

  1. A

    True

  2. B

    False