# Hyperbolic Trig Functions (in the works)

## Description

Sinh is called Hyperbolic Sine. Sinh and 5 other functions are analogous to the trig functions. They are defined this way:

`Sinh[x]:= ( E^2-E^(-x) )/2`

or`-I*Sin[I*x]`

`Cosh[x]:= ( E^2+E^(-x) )/2`

or`Cos[I*x]`

`Tanh[x]:= Sinh[x]/Cosh[x]`

or`-I*Tan[I*x]`

`Sech[x]:= 1/Cosh[x]`

`Csch[x]:= 1/Sinh[x]`

`Coth[x]:= Cosh[x]/Sinh[x]`

The E is the number
`Limit[(1 + 1/x)^x, x -> Infinity]`

~= 2.71828. The capital I denotes the complex number
`Sqrt[-1]`

.

They are called hyperbolic trig functions because they bear strong similarities to the trig functions. Trig functions relate to a circle, while hyperbolic trig functions relate to a rectangular hyperbola x^-y^==1 in a similar way. And all identies of trig functions have a analogue in the hyperbolic ones of the same form.

The hyperbolic cosine Cosh is famously known as catenary .