sinh

Hyperbolic sine

Syntax

Y = sinh(X)

Description

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

Examples

Hyperbolic Sine of Vector

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

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

Y = 1×4
103 ×

         0    0.0115    0.2677    6.1958

Graph of Hyperbolic Sine Function

Plot the hyperbolic sine over the domain $$-5\le x\le 5$$.

x = -5:0.01:5;
y = sinh(x);
plot(x,y)
grid on

Plot Hyperbolic Sine and Exponential Functions

The hyperbolic sine satisfies the identity $\sinh \left(\mathit{x}\right)=\frac{{\mathit{e}}^{\mathit{x}}-{\mathit{e}}^{-\mathit{x}}}{2}$. In other words, $\sinh \left(\mathit{x}\right)$ is half the difference of the functions ${\mathit{e}}^{\mathit{x}}$ and ${\mathit{e}}^{-\mathit{x}}$. Verify this by plotting the functions.

Create a vector of values between -3 and 3 with a step of 0.25. Calculate and plot the values of sinh(x), exp(x), and exp(-x). As expected, the sinh curve is positive where exp(x) is large, and negative where exp(-x) is large.

x = -3:0.25:3;
y1 = sinh(x);
y2 = exp(x);
y3 = exp(-x);
plot(x,y1,x,y2,x,y3)
grid on
legend('sinh(x)','exp(x)','exp(-x)','Location','bestoutside')

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 Sine

The hyperbolic sine of an angle x can be expressed in terms of exponential functions as

$$\sinh \left(x\right)=\frac{e^x-e^{-x}}{2}.$$

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

$$\sinh \left(x\right)=-i\sin \left(ix\right).$$

Extended Capabilities

Tall Arrays

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

The sinh 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 sinh 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 sinh 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.