## Friday, October 21, 2011

### Hyperbolic Cosine & Hyperbolic Secant

The hyperbolic cosine function is defined as
$\cosh(x)=\frac{e^{x} +e^{-x}}{2}$

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

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

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Now, take a look at the graph of the reciprocal of hyperbolic cosine function, i.e. hyperbolic secant function, which is defined as
$\textup{sech}(ax)=\frac{1}{\cosh(x)}=\frac{2}{e^{ax} +e^{-ax}}$

Observe that when a = 1,

Again, slide the value of 'a' to view the changes of the graph.

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Betty, Created with GeoGebra