# Cos 2 Theta Calculator

Omni's **cos 2 theta calculator** is here to help you whenever you have to deal with double angles and cosines.

In the article below we explain where the **cos 2 theta identity** comes from and what formula for cos 2 theta you should use depending on your data, i.e., whether you know the cosine of half the angle or rather its sine. We also discuss **how to find cos 2 theta using this calculator** and show you **similar Omni tools**, so that you can learn even more!

## Formula for cos 2 theta

The formula for the cosine of a double angle is a **trigonometric identity** allowing us to quickly determine the value of the cosine of an angle if we know the cosine or sine value of half of the angle.

The cos 2 theta, or, to write it in a more beautiful way, $\cos(2\theta)$ identity reads

Using the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) =1$, we can substitute $\cos^2(\theta)$ with $1-\sin^2(\theta)$, obtaining

Alternatively, we can substitute $\sin^2(\theta)$ with $1-\cos^2(\theta)$, which gives

You can choose any of these cos 2 theta identities to solve your *cos of double angle* problem. Make your choice based on what data is given or... just use Omni's cos 2 theta calculator!

## How to use this cos 2 theta calculator?

To use this tool to find cos 2 theta, you only need to enter the angle θ and... admire the result. As for entering the angle, you have three options:

- degrees;
- radians; and
- pi times radians.

Use the last option to input angles like $\frac \pi6$ or $\frac 3 4\pi$.

🙋 Although the focus of this tool is on the cos 2 theta identity, you can easily switch it to compute the double angle trig formula for sine and tangent as well!

## Omni double angle calculators

Happy with the cos 2 theta calculator? Omni features a whole collection of tools dedicated to the double angle trig identities:

## FAQ

### How do I find cos 4 theta given cos theta?

To calculate cos(4θ) from cos(θ), use the double angle formula twice:

- Calculate
`cos(2θ)= 2cos²(θ) - 1`

. - Calculate
`cos(4θ)= 2cos²(2θ) - 1`

- So the final formula reads
`cos(4θ)= 2(2cos²(θ) - 1)² - 1`

. - If you're given
`sin(θ)`

instead of`cos(θ)`

, follow the same steps but use the formula`cos(2θ)= 1- 2sin²(θ)`

.

### What is the value of cos(40°) given sin(20°)?

The value of `cos(40°)`

is `0.766`

. To arrive at this result, we find cos 2 theta via the formula `cos(2θ)= 1 - 2sin²(θ)`

for `θ = 20°`

. Plugging in `sin(20°) = 0.342`

, we obtain `cos(2θ)= 1 - 2×0.342² = 0.766`

, as claimed.

*Input the angle...*