## Sunday, July 22, 2012

### Hyperbolic Functions - I

Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" and the hyperbolic cosine "cosh" from which are derived the hyperbolic tangent "tanh" and so on, corresponding to the derived trigonometric functions.

Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola.
The hyperbolic functions cosh x and sinh x are deļ¬ned using the exponential function ex. Following are the definitions of cosh x , sinh x and tanh x.

cosh x = (ex+ e-x)/2
sinh x = (ex - e-x)/2
tanh x = (ex - e-x)/(ex + e-x)
Hyperbolic sine and cosine satisfy the identity cosh2 - sinh2=1
Select the check box in the following applet to view graph of function.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com