Initial Publication Date: July 19, 2011

# 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?**

**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. **

**Problem 4. What is the sine of angle A?**

Recall that

`text{Sin}=\frac{text{Opposite}}{text{Hypotenuse}`

so,

`text{Sin(A)} = \frac{3000 m}{6000 m}`

**Problem 5.** **Determine angle A in degrees.**

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**.

**Problem 6.** **What is the cosine of angle B?**
Recall that

`text{Cos}=\frac{text{Adjacent}}{text{Hypotenuse}`

so, substituting appropriate numbers for the adjacent and hypotenuse, you can calculate the cos of B,

`text{Cos(B)}=\frac{3000 m}{6000 m}`