NumicornNumicornLearn, solve, progress

Trigonometric Functions Practice Tests

These Grade 11 Math practice tests build fluency with the unit circle, degree-radian conversions, trigonometric ratios and identities, graph transformations, equations, inverse functions, and triangle applications.

Skills covered

  • Evaluating sine, cosine, tangent, and reciprocal functions on the unit circle
  • Converting between degrees and radians and identifying quadrant signs
  • Using Pythagorean, reciprocal, quotient, and symmetry identities
  • Analyzing amplitude, period, midline, shifts, range, and trig graphs
  • Solving trigonometric equations and applying right-triangle ratios, arc length, sector area, and the Laws of Sines and Cosines

How to use these practice tests

Keep angle units consistent, locate the reference angle and quadrant, select the appropriate identity or ratio, and check that the solution lies in the stated interval.

For more Grade 11 Math practice, return to the Grade 11 Math category.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

3. Test

Grade 11 Trigonometric Functions Practice Tests

Practice Grade 11 Math questions about the unit circle, radians, trigonometric ratios, identities, graphs, equations, inverse functions, and triangle applications.

Choose the best answer. Use radians or degrees consistently, identify the reference angle and quadrant, and verify trig equations and triangle relationships.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the period of y=sin⁡xy=\sin x?

Please select an answer first.

Correct answer: A

The correct answer is 2π2\pi.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sine repeats after one full revolution, or 2pi radians.
  3. Check the result: The correct answer is 2π2\pi.

Sine repeats after one full revolution, or 2pi radians.

2. QuestionMultiple choice

What is the amplitude of y=3sin⁡xy=3\sin x?

Please select an answer first.

Correct answer: B

The correct answer is 3.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The amplitude is the absolute value of the coefficient of sine, |3|=3.
  3. Check the result: The correct answer is 3.

The amplitude is the absolute value of the coefficient of sine, |3|=3.

3. QuestionMultiple choice

What is the midline of y=2cos⁡x+2y=2\cos x+2?

Please select an answer first.

Correct answer: C

The correct answer is y=2y=2.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The vertical shift is 2, so the midline is y=2.
  3. Check the result: The correct answer is y=2y=2.

The vertical shift is 2, so the midline is y=2.

4. QuestionMultiple choice

How is y=sin⁡(x−π2)y=\sin(x-\frac{\pi}{2}) shifted from y=sin⁡xy=\sin x?

Please select an answer first.

Correct answer: D

The correct answer is Right π2\frac{\pi}{2}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Replacing x with x-pi/2 shifts the graph right pi/2.
  3. Check the result: The correct answer is Right π2\frac{\pi}{2}.

Replacing x with x-pi/2 shifts the graph right pi/2.

5. QuestionMultiple choice

Where does y=cos⁡xy=\cos x attain its maximum at the starting point?

Please select an answer first.

Correct answer: A

The correct answer is x=0x=0.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Cosine starts at its maximum value 1 when x=0.
  3. Check the result: The correct answer is x=0x=0.

Cosine starts at its maximum value 1 when x=0.

6. QuestionMultiple choice

What is the amplitude of y=2sin⁡xy=2\sin x?

Please select an answer first.

Correct answer: B

The correct answer is 2.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The amplitude is the absolute value of the sine coefficient.
  3. Check the result: The correct answer is 2.

The amplitude is the absolute value of the sine coefficient.

7. QuestionMultiple choice

What is the period of y=tan⁡xy=\tan x?

Please select an answer first.

Correct answer: C

The correct answer is π\pi.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Tangent repeats after pi radians.
  3. Check the result: The correct answer is π\pi.

Tangent repeats after pi radians.

8. QuestionMultiple choice

What is the period of y=sin⁡(2x)y=\sin(2x)?

Please select an answer first.

Correct answer: D

The correct answer is π\pi.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: For sin(Bx), the period is 2pi/|B|, so 2pi/2=pi.
  3. Check the result: The correct answer is π\pi.

For sin(Bx), the period is 2pi/|B|, so 2pi/2=pi.

9. QuestionMultiple choice

What transformation changes y=cos⁡xy=\cos x into y=−cos⁡xy=-\cos x?

Please select an answer first.

Correct answer: A

The correct answer is Reflection across the x-axis.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Multiplying all outputs by -1 reflects the graph across the x-axis.
  3. Check the result: The correct answer is Reflection across the x-axis.

Multiplying all outputs by -1 reflects the graph across the x-axis.

10. QuestionMultiple choice

What is the range of y=sin⁡x+1y=\sin x+1?

Please select an answer first.

Correct answer: B

The correct answer is 0≤y≤20\le y\le2.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sine ranges from -1 to 1; shifting up 1 gives a range from 0 to 2.
  3. Check the result: The correct answer is 0≤y≤20\le y\le2.

Sine ranges from -1 to 1; shifting up 1 gives a range from 0 to 2.

Previous testNext test