# Cosine Calculator

URL: https://speedycalculator.com/calculators/math/cos/
Last updated: 2026-10-30

> The cosine calculator finds cos α for any angle in degrees, radians or multiples of π, with the exact value for multiples of 15° and the five other trigonometric functions of the same angle.

## Inputs

- Angle unit
- Angle α

## Results

- cos(α)
- sin(α)
- tan(α)
- csc(α)
- sec(α)
- cot(α)

## Formula

```
cos α = adjacent / hypotenuse = x-coordinate on the unit circle
Range: [−1, 1] · Domain: all real numbers · Period: 2π (360°)
```

## Explanation

The cosine of an angle is the ratio of the adjacent side to the hypotenuse; on the unit circle it is the x-coordinate. Cosine gives the horizontal component of forces and velocities, and appears in the law of cosines, dot products and Fourier series.

### How to use the Cosine Calculator

- **Angle unit**
- **Angle α**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Enter the angle and pick its unit. The angle is converted to radians and cos is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.

## Worked example

Inputs — Angle unit: Degrees (°); Angle α: 30.

Results — **cos(α) = √3/2 ≈ 0.8660254038**; sin(α) = 1/2 ≈ 0.5; tan(α) = √3/3 ≈ 0.5773502692; csc(α) = 2; sec(α) = 1.154700538; cot(α) = 1.732050808.

## Key terms

- **Cosine**: cos α = adjacent / hypotenuse = x-coordinate on the unit circle.
- **Exact value**: A value written with integers and square roots instead of decimals.

## FAQ

**What is cos 60°?**
Exactly 1/2.

**Is cosine even or odd?**
Even: cos(−α) = cos α.

**Where is cosine negative?**
In quadrants II and III.

**How are sine and cosine related?**
cos α = sin(90° − α), and sin²α + cos²α = 1.


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)
- [Wolfram MathWorld – Cosine](https://mathworld.wolfram.com/Cosine.html)