## Friday, October 21, 2011

### Hyperbolic Sine & Hyperbolic Cosecant

The hyperbolic sine function is defined as
$\sinh (x)=\frac{e^x -e^{-x}}{2}$

or generally,
$\sinh (ax)=\frac{e^{ax} -e^{-ax}}{2}$

Look at the graph below, try to slide the value of 'a' to different values to view the changes on graph.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Now, take a look at the graph of the reciprocal of hyperbolic sine function, i.e. hyperbolic cosecant function, which is defined as
$\textup{csch} \; (ax)=\frac{1}{\sinh{ax}}=\frac{2}{e^{ax} -e^{-ax}}$.

Observe that when a =1,
Again, slide the value of 'a' to view the changes of the graph.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Betty, Created with GeoGebra