# atan

## Syntax

• ``Y = atan(X)``
example

## Description

example

````Y = atan(X)` returns the Inverse Tangent (tan-1) of the elements of `X`. The `atan` function operates element-wise on arrays. For real elements of `X`, `atan(X)` returns values in the interval `[-pi/2,pi/2]`. For complex values of `X`, `atan(X)` returns complex values. All angles are in radians.```

## Examples

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### Inverse Tangent of a Value

`atan(0.8)`
```ans = 0.6747```

### Inverse Tangent of a Vector of Complex Values

Find the inverse tangent of the elements of vector `x`. The `atan` function acts on `x` element-wise.

```x = [0.5i 1+3i -2.2+i]; Y = atan(x)```
```Y = 0.0000 + 0.5493i 1.4615 + 0.3059i -1.2019 + 0.1506i```

### Plot the Inverse Tangent Function

Plot the inverse tangent function over the interval .

```x = -20:0.01:20; plot(x,atan(x)) grid on ```

## Input Arguments

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### `X` — Numeric inputnumber | vector | matrix | multidimensional array

Numeric input, specified as a number, vector, matrix, or multidimensional array.

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

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### Inverse Tangent

The inverse tangent is defined as

${\mathrm{tan}}^{-1}\left(z\right)=\frac{i}{2}\mathrm{log}\left(\frac{i+z}{i-z}\right).$