atan2
Fourquadrant inverse tangent
Syntax
Description
P = atan2(
returns the
fourquadrant inverse
tangent (tan^{1}) of Y
,X
)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
).
Examples
Find FourQuadrant Inverse Tangent of a Point
Find the fourquadrant inverse tangent of the point y = 4
, x = 3
.
atan2(4,3)
ans = 2.2143
Convert Complex Number to Polar Coordinates
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 FourQuadrant Inverse Tangent
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
Y
— ycoordinates
scalar  vector  matrix  multidimensional array  table  timetable
ycoordinates, 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
byN
matrix and
X
is a scalar or
1
byN
row vector). For more
information, see Compatible Array Sizes for Basic Operations.
Data Types: single
 double
 table
 timetable
X
— xcoordinates
scalar  vector  matrix  multidimensional array  table  timetable
xcoordinates, 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
byN
matrix and
X
is a scalar or
1
byN
row vector). For more
information, see Compatible Array Sizes for Basic Operations.
Data Types: single
 double
 table
 timetable
More About
FourQuadrant Inverse Tangent
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) 


atan2(0,0) 


Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
This function fully supports tall arrays. For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
If you use
atan2
with single type and double type operands, the generated code might not produce the same result as MATLAB. See Binary ElementWise Operations with Single and Double Operands (MATLAB Coder).
GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.
ThreadBased Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports threadbased environments. For more information, see Run MATLAB Functions in ThreadBased Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced before R2006aR2023a: Perform calculations directly on tables and timetables
The atan2
function can calculate on all variables within a table or
timetable without indexing to access those variables. All variables must have data types
that support the calculation. For more information, see Direct Calculations on Tables and Timetables.
Open Example
You have a modified version of this example. Do you want to open this example with your edits?
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
 América Latina (Español)
 Canada (English)
 United States (English)
Europe
 Belgium (English)
 Denmark (English)
 Deutschland (Deutsch)
 España (Español)
 Finland (English)
 France (Français)
 Ireland (English)
 Italia (Italiano)
 Luxembourg (English)
 Netherlands (English)
 Norway (English)
 Österreich (Deutsch)
 Portugal (English)
 Sweden (English)
 Switzerland
 United Kingdom (English)