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Hyperbolic sine



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.


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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

Plot the hyperbolic sine over the domain -5x5.

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

Figure contains an axes. The axes contains an object of type line.

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);
grid on

Figure contains an axes. The axes contains 3 objects of type line. These objects represent sinh(x), exp(x), exp(-x).

Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

More About

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Hyperbolic Sine

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

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

See Also

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Introduced before R2006a