# tanh

Hyperbolic tangent

## Description

example

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

## Examples

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

X = [0 pi 2*pi 3*pi];
Y = tanh(X)
Y = 1×4

0    0.9963    1.0000    1.0000

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

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

## 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

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### Hyperbolic Tangent

The hyperbolic tangent of an angle x is the ratio of the hyperbolic sine and hyperbolic cosine

$\mathrm{tanh}\left(x\right)=\frac{\mathrm{sinh}\left(x\right)}{\mathrm{cosh}\left(x\right)}=\frac{{e}^{2x}-1}{{e}^{2x}+1}.$

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

$\mathrm{tanh}\left(x\right)=-i\mathrm{tan}\left(ix\right)\text{\hspace{0.17em}}.$