# 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?**

- Type
*35*into your calculator - press the
**sin**button.

- Your calculator should read
**0.574**.

If you do not get the correct answer, check to make sure that your calculator is in degree mode.

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

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

- Type
*12*into your calculator

- press the
**cos**button.

- Your calculator should read
**0.978**.

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

- Type
*75*into your calculator

- press the
**tan**button.

- Your calculator should read
**0.0879**.

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

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

**Problem 4.**

**What is the sine of angle A?**

**Problem 5.**

**Determine angle A in degrees.**

Since you determined that

you can then rearrange this equation to solve for A:

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

**sin(A)= 0.5**in the problem above,you can then rearrange this equation to solve for A:

**sin**,^{-1}(0.5)= Acalculate 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**(sometimes shift) on your calculator and then the^{nd}**sin**button.

This produces*sin*on the calculator screen.^{-1} - Enter 0.5 after the
*sin*.^{-1} - Hit
**enter**or**=**and the result should be**30 degrees**.

Problem 6.

Problem 6.

**What is the cosine of angle B?**