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.

example

Examples

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Inverse Tangent of a Value

Open Live Script

Find the inverse tangent of a value.

atan(0.8)

ans = 
0.6747

Inverse Tangent of a Vector of Complex Values

Open Live Script

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

Open Live Script

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

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

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

Input Arguments

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`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

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Inverse Tangent

The inverse tangent is defined as

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

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

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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

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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.

atan

Syntax

Description

Examples

Inverse Tangent of a Value

Inverse Tangent of a Vector of Complex Values

Plot the Inverse Tangent Function

Input Arguments

X — Tangent of angle scalar | vector | matrix | multidimensional array | table | timetable

More About

Inverse Tangent

Extended Capabilities

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

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.

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

Distributed Arrays Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

R2023a: Perform calculations directly on tables and timetables

See Also

`X` — Tangent of angle
scalar | vector | matrix | multidimensional array | table | timetable

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

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`.

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

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.