# Cosine Triangle Calculator

The powerful cosine triangle calculator (also "cos calc") is a tool that determines the cosine of an angle that can be expressed in degrees, radians, or pi radians—wondering how you will solve that trigonometry homework? Don't worry. In this article, **we will explain what cosine is, how to calculate it, and will show several examples.**

## What is the cosine in Trigonometry?

The cosine of an angle is a trigonometric function that relates both triangle sides that build the angle. It's better to explain it with an image:

As you can see, $\alpha$ is the angle between the $b$ and the $c$ side of the triangle. Then, the cosine of alpha is the division between $b$ and $c$.

Note that $c$ is the hypotenuse of the triangle. So the cosine definition can be expressed as follows:

In a right triangle, **the cosine is the trigonometric function that divides one side of the angle and the hypotenuse.** Such side and the hypotenuse are the ones that build the angle we are referring to.

## How to calculate the cosine of an angle?

To calculate the cosine is pretty straightforward. You can use our cosine calculator or do the following:

- Pick the hypotenuse value and the other side that builds the angle. In the above picture, we have represented them as $b$ and the $c$.
- Divide $b$ by $c$. The result is the cosine of the angle. Note value can never go over 1.

## Cosine triangle example - What is the cosine of 30 degrees?

**It is 0.866.** Also, it is the square root of three divided by 2. How? Try Omnicalculator's tool cosine triangle calculator or do the following:

- Recognize you have a 30-60 right triangle. This one is special because all the sides are in constant relationship. The hypotenuse is equivalent to 2; meanwhile, the other sides are equivalent to 1 and $\footnotesize \sqrt{3}$
- The 30 degrees angle is built by the $\footnotesize \sqrt{3}$ side and the hypotenuse. Thus, we divide both sides and get the cosine: 0.866.

## Other useful tools like the cosine triangle calculator

Since you already know how to use this cosine calculator, you can take a look at other calculators:

## FAQ

### How do you get the cosine of an angle?

Try Omnicalculator's tool cosine triangle calculator or do the following:

**Pick the hypotenuse and the other side that builds the angle.**Let's call it`c`

and`b`

, respectively.**Divide the side by the hypotenuse**, which means`b`

by`c`

.- The result is the cosine of the angle. Verify you do not get a result over 1.

### What is the cosine of 45 degrees?

0.707. **We get it by dividing the side of a 45 degrees right triangle** (equivalent to 1) **and its hypotenuse** (equivalent to the square root of 2).