# atan2

## 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. The `atan2` function acts on `Y` and `X` element-wise to return `P`, which is the same size as `Y` and `X`.```

## Examples

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### Find Four-Quadrant Inverse Tangent of a Point

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

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

### Convert Complex Number to Polar Coordinates

Convert `4 + 3i` into polar coordinates.

```z = 4 + 3i; r = abs(z) theta = atan2(imag(z),real(z)) ```
```r = 5 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` — Real valued inputnumber | vector | matrix | multidimensional array

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

Data Types: `single` | `double`

### `X` — Real valued inputnumber | vector | matrix | multidimensional array

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

Data Types: `single` | `double`

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The four-quadrant tangent inverse, `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 which are limited to the interval `[-pi/2,pi/2]`, which is the right side of this diagram.