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 .
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 . In other words, is half the difference of the functions and . 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
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')
X — Input angles in radians
scalar | vector | matrix | multidimensional array
Input angles in radians, specified as a scalar, vector, matrix, or multidimensional array.
Complex Number Support: Yes
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
Calculate with arrays that have more rows than fit in memory.
This function fully supports tall arrays. For more information, see Tall Arrays.
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This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
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).
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This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).