Hyperbolic Cosine & Hyperbolic Secant

The hyperbolic cosine function is defined as

or generally,
.

Look at the graphs below, the blue solid curve is the curve of  , whereas the dotted curves are the graphs of its terms. If you can't remember the graph of , you can try to add up the y-values of the two terms (dotted curves) and get the y-value of .

Try to slide the value of a to different values to view the changes of the graphs.



Now, take a look at the graph of the reciprocal of hyperbolic cosine function, i.e. hyperbolic secant function, which is defined as

Observe that when a = 1,

1. as , , thus ;
2. as , , thus;
3. as , , thus .

Again, slide the value of a to view the changes of the graphs.


Betty, Created with GeoGebra