Accelerating the pace of engineering and science

# atan2

## 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

expand all

### 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

expand all

### 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