## ATAN2 Inverse Trigonometric 4-Quadrant Arctangent Function

Section: Mathematical Functions

### Usage

Computes the`atan2`

function for its argument. The general
syntax for its use is
z = atan2(y,x)

where `x`

and `y`

are `n`

-dimensional arrays of numerical type.
Integer types are promoted to the `double`

type prior to
calculation of the `atan2`

function. The size of the output depends
on the size of `x`

and `y`

. If `x`

is a scalar, then `z`

is the same size as `y`

, and if `y`

is a scalar, then `z`

is the same size as `x`

. The type of the output is equal to the type of
|y/x|.

### Function Internals

The function is defined (for real values) to return an angle between`-pi`

and `pi`

. The signs of `x`

and `y`

are used to find the correct quadrant for the solution. For complex
arguments, the two-argument arctangent is computed via

For real valued arguments `x,y`

, the function is computed directly using
the standard C library's numerical `atan2`

function. For both
real and complex arguments `x`

, note that generally

due to the periodicities of `cos(x)`

and `sin(x)`

.

### Example

The following code demonstates the difference between the`atan2`

function and the `atan`

function over the range `[-pi,pi]`

.
--> x = linspace(-pi,pi); --> sx = sin(x); cx = cos(x); --> plot(x,atan(sx./cx),x,atan2(sx,cx))

Note how the two-argument `atan2`

function (green line)
correctly ``unwraps'' the phase of the angle, while the `atan`

function (red line) wraps the angle to the interval `[-\pi/2,\pi/2]`

.