# atan2

## Purpose

Four-quadrant inverse tangent.

## Synopsis

    P = atan2(Y,X)

## Description

`atan2(Y,X)` returns a matrix `P` the same size as `X` and `Y` containing the element-by-element, four-quadrant arctangent of the real parts of `Y` and `X`. Any imaginary parts are ignored.

Elements of `P` are in the interval `[-pi, pi]`. The specific quartile is determined by `sign(Y)` and `sign(X)`:

This contrasts with the result of `atan(Y/X)`, which is limited to the interval `[-pi/2, pi/2]`, or the right side of this diagram.

## Examples

Any complex number z = x+iy can be written in polar coordinates with

    r = abs(z)
    theta = atan2(imag(z),real(z))

Then `z` is equal to

    r *exp(i *theta)

This is a common operation, so MATLAB provides a function, `angle(z)`, that simply computes `atan2(imag(z),real(z))`.

## See Also

     abs, angle, cos, funm, sin, tan

(c) Copyright 1994 by The MathWorks, Inc.