Hyperbolic functions/R/Introduction/Section
![](http://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Sinh-cosh-r-28pt.svg/230px-Sinh-cosh-r-28pt.svg.png)
The function defined for by
The function defined for by
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Catenary-pm.svg/230px-Catenary-pm.svg.png)
The functions hyperbolic sine and hyperbolic cosine
have the following properties.Proof
See exercise.
The function hyperbolic sine is strictly increasing, and the function hyperbolic cosine is strictly decreasing on and strictly increasing on .
![](http://upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hyperbolic_Tangent.svg/230px-Hyperbolic_Tangent.svg.png)
The function