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sinh

Hyperbolic sine

Syntax


            
             Y = sinh(X)

Description

example

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

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Hyperbolic Sine of Vector

Open Live Script

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

Open Live Script

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

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

Plot Hyperbolic Sine and Exponential Functions

Open Live Script

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

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`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

collapse all

Hyperbolic Sine

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

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

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

$\sinh (x) = - i \sin (i x) .$

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™.

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™.

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 R2006a

expand all

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 .

sinh (adsbygoogle = window.adsbygoogle || []).push({});

Syntax

Description

Examples

Hyperbolic Sine of Vector

Graph of Hyperbolic Sine Function

Plot Hyperbolic Sine and Exponential Functions

Input Arguments

X — Input angles in radians (adsbygoogle = window.adsbygoogle || []).push({}); scalar | vector | matrix | multidimensional array | table | timetable

More About

Hyperbolic Sine

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

sinh

`X` — Input angles in radians
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™.