Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

atan2

Four-quadrant inverse tangent

Syntax

Description

example

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

Examples

collapse all

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

collapse all

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

More About

collapse all

Four-Quadrant Inverse Tangent

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.

Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.

See Also

| | | |

Introduced before R2006a

Was this topic helpful?