    # tanh

This function computes the hyperbolic tan of a number.

# TANH

## NAME

tanh - This function computes the hyperbolic tan of a number.

tanh(number)

## DESCRIPTION

This mathematical function allows the user to compute the hyperbolic tan of an argument defined between -infinity to infinity. The answer has to be between -1 and 1. This is not a periodic function, unlike its basis function: the tan function. It returns a value only in the 1st or the 3rd quadrant of the xy plane, meaning that if x<0, y<0, and if x>0, y>0. The tanh function is defined as tanh x = ( exp(x) - exp(-x))/(exp(x)+exp(-x)), so tanhx= sinh(x)/cosh(x) and tanh(x)=-itan(ix).

## PARAMETERS

number
Specify the number (float) used as argument for the tanh function.

## RETURN

The tanh value of the argument.

## EXAMPLES

Note: In the followings examples, the _ between the { should be removed to make it work.

```One can use this function with positive integers:

test(q(res={_{tanh(1);}}.),q(res=.761594.));

With negative integers:

test(q(res={_{tanh(-1);}}.),q(res=-.761594.));

Note that tanh(-x)=-tanh(x).

With big integers:

test(q(res={_{tanh(45);}}.),q(res=1.));

With other variables:

test(q(res={_{
%include "/includes/extenso.sn";
a=0;
tanh(a);
}}.),
q(res=0.));

With another trigonometric function:

test(q(res={_{
%include "/includes/extenso.sn";
a=sin(0);
tanh(a);
}}.),
q(res=0.));

With an array:

test(q(res={_{tanh(1,0,-1);}}.),q(res=\[.761594,0,-.761594\].));
```