Initial Publication Date: July 19, 2011 | Revision: September 19, 2024 (see revision history: 2 events)

Basic Trig Functions: Practice Problems

These problems are designed to help you learn basic trigonometry ("trig") functions and how to use your calculator correctly.
Try solving these on your own (without peaking at the solutions). You may want to download a sheet with all the questions (Acrobat (PDF) 33kB Jul25 09) to print out and try. If you need help, look at the hidden solutions. You may use a calculator.

Calculating Sine, Cosine, and Tangent

Problem 1. The angle of repose for sand is typically about 35°. What is the sine of this angle?

Show solution

Problem 2. When driving, a steep hill is typically only 12°. What is the cosine of this angle?

Show solution

Problem 3. The angle that waves hit a shoreline is 75°. What is the tangent of this angle?

Show solution

For the next three problems, use the photo of Mount Rainier below.

Problem 4. What is the sine of angle A?

Show solution

Problem 5. Determine angle A in degrees.

Show next step to find A

Since you determined that

sin(A) = 0.5 in the problem above,

you can then rearrange this equation to solve for A:

sin^-1(0.5) = A,

calculate the angle on your calculator by taking the inverse sine of 0.5.

Depending on your calculator, you will typically need to press a button labeled 2^nd (sometimes shift) on your calculator and then the sin button.
This produces sin^-1 on the calculator screen.
Enter 0.5 after the sin^-1.
Hit enter or = and the result should be 30 degrees.