# Documentation

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# atan2

Four-quadrant inverse tangent

## Syntax

• ``P = atan2(Y,X)``
example

## Description

example

````P = atan2(Y,X)` returns the four-quadrant inverse tangent (tan-1) of `Y` and `X`, which must be real.```

## Examples

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Find the four-quadrant inverse tangent of the point `y = 4`, `x = -3`.

```atan2(4,-3) ```
```ans = 2.2143 ```

Convert `4 + 3i` into polar coordinates.

```z = 4 + 3i; r = abs(z) ```
```r = 5 ```
```theta = atan2(imag(z),real(z)) ```
```theta = 0.6435 ```

The radius `r` and the angle `theta` are the polar coordinate representation of `4 + 3i`.

Alternatively, use `angle` to calculate `theta`.

```theta = angle(z) ```
```theta = 0.6435 ```

Convert `r` and `theta` back into the original complex number.

```z = r*exp(i*theta) ```
```z = 4.0000 + 3.0000i ```

Plot `atan2(Y,X)` for `-4<Y<4` and `-4<X<4`.

Define the interval to plot over.

```[X,Y] = meshgrid(-4:0.1:4,-4:0.1:4); ```

Find `atan2(Y,X)` over the interval.

```P = atan2(Y,X); ```

Use `surf` to generate a surface plot of the function. Note that `plot` plots the discontinuity that exists at `Y=0` for all `X<0`.

```surf(X,Y,P); view(45,45); ```

## Input Arguments

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y-coordinates, specified as a scalar, vector, matrix, or multidimensional array. Inputs `Y` and `X` must either be the same size or have sizes that are compatible (for example, `Y` is an `M`-by-`N` matrix and `X` is a scalar or `1`-by-`N` row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: `single` | `double`

x-coordinates, specified as a scalar, vector, matrix, or multidimensional array. Inputs `Y` and `X` must either be the same size or have sizes that are compatible (for example, `Y` is an `M`-by-`N` matrix and `X` is a scalar or `1`-by-`N` row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: `single` | `double`

## More About

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### Four-Quadrant Inverse Tangent

The four-quadrant inverse tangent, `atan2(Y,X)`, returns values in the closed interval `[-pi,pi]` based on the values of `Y` and `X` as shown in the graphic.

In contrast, `atan(Y/X)` returns results that are limited to the interval `[-pi/2,pi/2]`, shown on the right side of the diagram.

### Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.

## See Also

#### Introduced before R2006a

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