# Documentation

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# atan2

P = atan2(Y,X)

## Description

example

P = atan2(Y,X) returns the four-quadrant inverse tangent (tan-1) of Y and X, which must be real.

## Examples

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

atan2(4,-3)
ans = 2.2143

Convert 4 + 3i into polar coordinates.

z = 4 + 3i;
r = abs(z)
r = 5
theta = atan2(imag(z),real(z))
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-coordinates, specified as a scalar, vector, matrix, or multidimensional array. Inputs Y and X must either be the same size or have sizes that are compatible (for example, Y is an M-by-N matrix and X is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: single | double

x-coordinates, specified as a scalar, vector, matrix, or multidimensional array. Inputs Y and X must either be the same size or have sizes that are compatible (for example, Y is an M-by-N matrix and X is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: single | double

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The four-quadrant inverse tangent, 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 that are limited to the interval [-pi/2,pi/2], shown on the right side of the diagram.