Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

# cos

Cosine of argument in radians

## Syntax

``Y = cos(X)``

## Description

````Y = cos(X)` returns the cosine for each element of `X`. The `cos` function operates element-wise on arrays. The function accepts both real and complex inputs. For purely real values or imaginary values of `X`, `cos` returns real values in the interval [-1 ,1]. For complex values of `X`, `cos` returns complex values. All angles are in radians.```

## Examples

collapse all

Plot the cosine function over the domain .

```x = -pi:0.01:pi; plot(x,cos(x)) grid on```

Calculate the cosine of the complex angles in vector `x`.

```x = [-i pi+i*pi/2 -1+i*4]; y = cos(x)```
```y = 1×3 complex 1.5431 + 0.0000i -2.5092 - 0.0000i 14.7547 +22.9637i ```

## Input Arguments

collapse all

Input angle in radians, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: `single` | `double`
Complex Number Support: Yes

## Output Arguments

collapse all

Cosine of input angle, returned as a real-valued or complex-valued scalar, vector, matrix or multidimensional array.

## More About

collapse all

### Cosine Function

The cosine of an angle, α, defined with reference to a right angled triangle is

The cosine of a complex argument, α, is

`$\text{cos}\left(\alpha \right)=\frac{{e}^{i\alpha }+{e}^{-i\alpha }}{2}\text{\hspace{0.17em}}.$`

Download eBook