sinh - Hyperbolic sine - MATLAB (original) (raw)

Main Content

Syntax

Description

Y = sinh([X](#d126e1670994)) 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.

example

Examples

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

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

Y = 1×4 103 ×

     0    0.0115    0.2677    6.1958

Plot the hyperbolic sine over the domain -5≤x≤5.

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

The hyperbolic sine satisfies the identity sinh(x)=ex-e-x2. In other words, sinh(x) is half the difference of the functions ex 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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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

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

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

Extended Capabilities

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

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).

Version History

Introduced before R2006a

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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.