MATLAB Function Reference

atan2

Four-quadrant inverse tangent

Syntax

P = atan2(Y,X)

Description

P = atan2(Y,X) returns an array P the same size as X and Y containing the element-by-element, four-quadrant inverse tangent (arctangent) of the real parts of Y and X. Any imaginary parts are ignored.

Elements of P lie in the closed interval [-pi,pi], where pi is MATLAB's floating- point representation of . The specific quadrant is determined by sign(Y) and sign(X):



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

Examples

Any complex number z = x+iy is converted to polar coordinates with

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

To convert back to the original complex number:

z = 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

atan, atanh, tan, tanh

atan, atanh

auread