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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.

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1. 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 sin⁡0\sin 0?

Please select an answer first.

Correct answer: A

The correct answer is 0.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: On the unit circle, the point at angle 0 has y-coordinate 0, so sin 0 = 0.
  3. Check the result: The correct answer is 0.

On the unit circle, the point at angle 0 has y-coordinate 0, so sin 0 = 0.

2. QuestionMultiple choice

What is cos⁡(π3)\cos\left(\frac{\pi}{3}\right)?

Please select an answer first.

Correct answer: B

The correct answer is 12\frac{1}{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 unit-circle value for cosine at pi/3 is the x-coordinate 1/2.
  3. Check the result: The correct answer is 12\frac{1}{2}.

The unit-circle value for cosine at pi/3 is the x-coordinate 1/2.

3. QuestionMultiple choice

What is tan⁡(π4)\tan\left(\frac{\pi}{4}\right)?

Please select an answer first.

Correct answer: C

The correct answer is 1.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: At pi/4, sine and cosine are both sqrt(2)/2, so their ratio is 1.
  3. Check the result: The correct answer is 1.

At pi/4, sine and cosine are both sqrt(2)/2, so their ratio is 1.

4. QuestionMultiple choice

What is sin⁡(π2)\sin\left(\frac{\pi}{2}\right)?

Please select an answer first.

Correct answer: D

The correct answer is 1.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: At pi/2, the unit-circle y-coordinate is 1.
  3. Check the result: The correct answer is 1.

At pi/2, the unit-circle y-coordinate is 1.

5. QuestionMultiple choice

What is cos⁡π\cos\pi?

Please select an answer first.

Correct answer: A

The correct answer is -1.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: At pi radians, the unit-circle point is (-1,0), so cosine is -1.
  3. Check the result: The correct answer is -1.

At pi radians, the unit-circle point is (-1,0), so cosine is -1.

6. QuestionMultiple choice

Convert 180∘180^\circ to radians.

Please select an answer first.

Correct answer: B

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: A straight angle is pi radians, so 180 degrees equals pi.
  3. Check the result: The correct answer is π\pi.

A straight angle is pi radians, so 180 degrees equals pi.

7. QuestionMultiple choice

Convert 3π2\frac{3\pi}{2} radians to degrees.

Please select an answer first.

Correct answer: C

The correct answer is 270∘270^\circ.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Multiply by 180/pi: (3pi/2)(180/pi)=270 degrees.
  3. Check the result: The correct answer is 270∘270^\circ.

Multiply by 180/pi: (3pi/2)(180/pi)=270 degrees.

8. QuestionMultiple choice

In which quadrant are sine and cosine both negative?

Please select an answer first.

Correct answer: D

The correct answer is Quadrant III.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: In Quadrant III, both the x- and y-coordinates on the unit circle are negative, while tangent is positive.
  3. Check the result: The correct answer is Quadrant III.

In Quadrant III, both the x- and y-coordinates on the unit circle are negative, while tangent is positive.

9. QuestionMultiple choice

What point on the unit circle corresponds to angle 0?

Please select an answer first.

Correct answer: A

The correct answer is (1,0)(1,0).

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The unit circle starts at the point (1,0) when the angle is 0.
  3. Check the result: The correct answer is (1,0)(1,0).

The unit circle starts at the point (1,0) when the angle is 0.

10. QuestionMultiple choice

What is cot⁡(π4)\cot\left(\frac{\pi}{4}\right)?

Please select an answer first.

Correct answer: B

The correct answer is 1.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Cotangent is cosine divided by sine, and both values at pi/4 are equal.
  3. Check the result: The correct answer is 1.

Cotangent is cosine divided by sine, and both values at pi/4 are equal.

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