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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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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

In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is the sine of the angle?

Please select an answer first.

Correct answer: A

The correct answer is 35\frac{3}{5}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sine is opposite divided by hypotenuse, so sin theta=3/5.
  3. Check the result: The correct answer is 35\frac{3}{5}.

Sine is opposite divided by hypotenuse, so sin theta=3/5.

2. QuestionMultiple choice

Which equation is the Law of Sines?

Please select an answer first.

Correct answer: B

The correct answer is asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The Law of Sines relates each side to the sine of its opposite angle.
  3. Check the result: The correct answer is asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}.

The Law of Sines relates each side to the sine of its opposite angle.

3. QuestionMultiple choice

Which equation is the Law of Cosines for side c?

Please select an answer first.

Correct answer: C

The correct answer is c2=a2+b2−2abcos⁡Cc^2=a^2+b^2-2ab\cos C.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: The included angle form of the Law of Cosines is c^2=a^2+b^2-2ab cos C.
  3. Check the result: The correct answer is c2=a2+b2−2abcos⁡Cc^2=a^2+b^2-2ab\cos C.

The included angle form of the Law of Cosines is c^2=a^2+b^2-2ab cos C.

4. QuestionMultiple choice

Two sides of a triangle are 3 and 4 with included angle π2\frac{\pi}{2}. What is the third side?

Please select an answer first.

Correct answer: D

The correct answer is 5.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: With a right angle, the Law of Cosines becomes the Pythagorean theorem: c=sqrt(3^2+4^2)=5.
  3. Check the result: The correct answer is 5.

With a right angle, the Law of Cosines becomes the Pythagorean theorem: c=sqrt(3^2+4^2)=5.

5. QuestionMultiple choice

If the opposite side is 10 and the adjacent side is 20, which equation finds the angle theta?

Please select an answer first.

Correct answer: A

The correct answer is θ=arctan⁡(1020)\theta=\arctan\left(\frac{10}{20}\right).

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Tangent uses opposite over adjacent, so theta=arctan(10/20), approximately 26.565 degrees.
  3. Check the result: The correct answer is θ=arctan⁡(1020)\theta=\arctan\left(\frac{10}{20}\right).

Tangent uses opposite over adjacent, so theta=arctan(10/20), approximately 26.565 degrees.

6. QuestionMultiple choice

What is the arc length for radius 6 and central angle π3\frac{\pi}{3}?

Please select an answer first.

Correct answer: B

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: For radians, arc length is s=r theta=6(pi/3)=2pi.
  3. Check the result: The correct answer is 2π2\pi.

For radians, arc length is s=r theta=6(pi/3)=2pi.

7. QuestionMultiple choice

What is the area of a sector with radius 4 and central angle π2\frac{\pi}{2}?

Please select an answer first.

Correct answer: C

The correct answer is 4π4\pi.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sector area is A=1/2 r^2 theta = 1/2(16)(pi/2)=4pi.
  3. Check the result: The correct answer is 4π4\pi.

Sector area is A=1/2 r^2 theta = 1/2(16)(pi/2)=4pi.

8. QuestionMultiple choice

Which trig function is usually used to model a quantity that oscillates periodically?

Please select an answer first.

Correct answer: D

The correct answer is Sine or cosine.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Sine and cosine functions repeat over regular intervals and model periodic behavior.
  3. Check the result: The correct answer is Sine or cosine.

Sine and cosine functions repeat over regular intervals and model periodic behavior.

9. QuestionMultiple choice

If the opposite and adjacent sides are 8 and 15, what is tan⁡θ\tan\theta?

Please select an answer first.

Correct answer: A

The correct answer is 815\frac{8}{15}.

  1. Identify the trigonometric structure: Determine the angle measure, ratio, identity, graph feature, equation, or triangle relationship involved.
  2. Apply the trigonometric relationship: Tangent is opposite divided by adjacent, so tan theta=8/15.
  3. Check the result: The correct answer is 815\frac{8}{15}.

Tangent is opposite divided by adjacent, so tan theta=8/15.

10. QuestionMultiple choice

How many radians are in one full rotation?

Please select an answer first.

Correct answer: B

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: A full circle measures 2pi radians.
  3. Check the result: The correct answer is 2π2\pi.

A full circle measures 2pi radians.

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