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atan2

Four-quadrant inverse tangent

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Syntax

P = atan2(Y,X)

Description

P = atan2(Y,X) returns the four-quadrant inverse tangent (tan-1) of Y and X, which must be real. The atan2 function follows the convention that atan2(x,x) returns 0 when x is mathematically zero (either 0 or -0).

example

Examples

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Open Live Script

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

atan2(4,-3)
ans = 
2.2143
Open Live Script

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
Open Live Script

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);

Figure contains an axes object. The axes object contains an object of type surface.

Input Arguments

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y-coordinates, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. 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 | table | timetable

x-coordinates, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. 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 | table | timetable

More About

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Four-Quadrant Inverse Tangent

The four-quadrant inverse tangent, atan2(Y,X), returns values in the closed interval [–π, π] based on the values of Y and X, as shown in the graphic.

Values returned by atan2(Y,X). For negative X and negative Y, atan2(Y,X) returns values in the interval (–π, –π/2). For positive X and negative Y, atan2(Y,X) returns values in the interval (–π/2, 0). For positive X and positive Y, atan2(Y,X) returns values in the interval (0, π/2). For negative X and positive Y, atan2(Y,X) returns values in the interval (π/2, π)

In contrast, atan(Y/X) returns results that are limited to the interval [–π/2, π/2], shown on the right side of the diagram.

IEEE Compliance

For real inputs, atan2 has a few behaviors that differ from those recommended in the IEEE®-754 Standard.

  MATLAB® IEEE
atan2(0,-0)

0

pi

atan2(-0,-0)

0

-pi

Extended Capabilities

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced before R2006a

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See Also

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