Practice Trigonometric Functions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Trigonometric functions (sin, cos, tan, etc.) relate angles in right triangles to side ratios and extend to periodic functions of real numbers via the unit circle.

Angles have numbers associated with them—sin, cos, tan capture different ratios.

Showing a random 20 of 50 problems.

Example 1

challenge
In triangle ABCABC, ∠A=30°\angle A = 30°, ∠B=105°\angle B = 105°, a=8a = 8. Find bb using the Law of Sines.

Example 2

hard
In triangle ABCABC, a=7a = 7, b=9b = 9, ∠C=60°\angle C = 60°. Find side cc using the Law of Cosines.

Example 3

hard
If sin⁡θ=35\sin\theta = \frac{3}{5} and θ\theta is in Quadrant II, find cos⁡θ\cos\theta and tan⁡θ\tan\theta.

Example 4

easy
Evaluate cos⁡0∘\cos 0^\circ.

Example 5

medium
If sin⁡θ=35\sin\theta=\frac{3}{5} and θ\theta is acute, find cos⁡θ\cos\theta.

Example 6

easy
In a right triangle, sin⁡θ=opposite?\sin\theta=\frac{\text{opposite}}{?}.

Example 7

medium
Evaluate sin⁡60∘+cos⁡30∘\sin 60^\circ+\cos 30^\circ.

Example 8

medium
Find the period of f(x)=sin⁡(2x)f(x)=\sin(2x).

Example 9

medium
Evaluate cos⁡(−60°)\cos(-60°).

Example 10

easy
What is the range of cos⁡x\cos x?

Example 11

easy
Evaluate sin⁡30∘\sin 30^\circ.

Example 12

easy
Evaluate cos⁡90°\cos 90°.

Example 13

easy
In a right triangle with legs 33 and 44 and hypotenuse 55, sin⁡θ\sin\theta for the angle opposite the side of length 33 is what?

Example 14

medium
Convert 210°210° to radians.

Example 15

challenge
Solve 2sin⁡2x−sin⁡x−1=02\sin^2 x-\sin x-1=0 for 0∘≤x<360∘0^\circ\le x<360^\circ.

Example 16

medium
If cos⁡θ=513\cos\theta=\frac{5}{13} and θ\theta acute, find tan⁡θ\tan\theta.

Example 17

medium
Evaluate sin⁡(−45°)\sin(-45°).

Example 18

easy
Evaluate sin⁡90∘\sin 90^\circ.

Example 19

easy
Evaluate tan⁡45∘\tan 45^\circ.

Example 20

medium
Evaluate sin⁡ ⁣(5π6)\sin\!\left(\dfrac{5\pi}{6}\right).
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