# cos

## 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 real values of `X`, `cos(X)` returns real values in the interval [-1, 1].For complex values of `X`, `cos(X)` returns complex values. ```

## Examples

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Plot the cosine function over the domain $-\pi \le x\le \pi$.

```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

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

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

## Output Arguments

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

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### Cosine Function

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

The cosine of a complex argument, α, is

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

## Tips

• To compute `cos(X*pi)` accurately, without using `pi` as a floating-point approximation of π, you can use the `cospi` function instead. For example, `cospi(m/2)` is exactly zero for odd integers `m` and `cospi(n)` is +1 or –1 for integers `n`.

## Version History

Introduced before R2006a

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