atan

Inverse tangent in radians

Syntax

Y = atan(X)

Description

Y = atan(X) returns the Inverse Tangent (tan^-1) of the elements of X in radians. The function accepts both real and complex inputs.

• For real values of X, atan(X) returns values in the interval [-π/2, π/2].

• For complex values of X, atan(X) returns complex values.

Examples

Inverse Tangent of a Value

Find the inverse tangent of a value.

atan(0.8)

ans = 
0.6747

Inverse Tangent of a Vector of Complex Values

Find the inverse tangent of the elements of vector x. The atan function acts on x element-wise.

x = [0.5i 1+3i -2.2+i];
Y = atan(x)

Y = 1×3 complex

   0.0000 + 0.5493i   1.4615 + 0.3059i  -1.2019 + 0.1506i

Plot the Inverse Tangent Function

Plot the inverse tangent function over the interval $$-20\le x\le 20$$.

x = -20:0.01:20; 
plot(x,atan(x))
grid on

Input Arguments

X — Tangent of angle

scalar | vector | matrix | multidimensional array | table | timetable

Tangent of angle, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. The atan operation is element-wise when X is nonscalar.

Data Types: single | double | table | timetable
Complex Number Support: Yes

More About

Inverse Tangent

The inverse tangent is defined as

$${\tan }^{-1}(z)=\frac{i}{2}\log \left(\frac{i+z}{i-z}\right).$$

This definition of the atan function returns angles in radians within the interval [-π/2, π/2]. To find the four-quadrant inverse tangent, where the returned angles are in the interval [-π, π], use atan2.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

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

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

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

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The atan function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). 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 R2006a

R2023a: Perform calculations directly on tables and timetables

The atan 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.