coth

Hyperbolic cotangent

Syntax

Y = coth(X)

Description

Y = coth(X) returns the hyperbolic tangent of the elements of X. The coth function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians.

Examples

Hyperbolic Cotangent of Vector

Create a vector and calculate the hyperbolic cotangent of each value.

X = [0 pi 2*pi 3*pi];
Y = coth(X)

Y = 1×4

       Inf    1.0037    1.0000    1.0000

Graph of Hyperbolic Cotangent

Plot the hyperbolic cotangent over the domain $$-\pi <x<0$$ and $$0<x<\pi$$.

x1 = -pi+0.01:0.01:-0.01; 
x2 = 0.01:0.01:pi-0.01;
y1 = coth(x1);
y2 = coth(x2);
plot(x1,y1,x2,y2)
grid on

Input Arguments

X — Input angles in radians

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

Input angles in radians, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

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

More About

Hyperbolic Cotangent

The hyperbolic cotangent of x is equal to the inverse of the hyperbolic tangent

$$\coth \left(x\right)=\frac{1}{\tanh \left(x\right)}=\frac{e^{2x}+1}{e^{2x}-1}.$$

In terms of the traditional cotangent function with a complex argument, the identity is

$$\coth \left(x\right)=i\cot \left(ix\right).$$

Extended Capabilities

Tall Arrays

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

The coth 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 coth 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 coth 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.