TITLE: Why do hyperbolic "trig" functions seem to be encountered rarely?
QUESTION [8 upvotes]: Hyperbolic "trig" functions such as $\sinh$, $\cosh$, have close analogies with regular trig functions such as $\sin$ and $\cos$. Yet the hyperbolic versions seem to be encountered relatively rarely. (My frame of reference is that of someone with college freshman/sophomore, but not advanced math.)
Why is that? Is it because the hyperbolic versions of these functions are less common/useful than the circular versions? 
Can you do the "usual" applications (Taylor series, Fourier series) with hyperbolic functions as you can with trigonometric?
I'm not a professional mathematician. I've had three semesters of calculus and one of linear algebra/differential equations, and "barely" know about hyperbolic functions. The question is with that frame of reference.

REPLY [2 votes]: Tom,
Anon's answer is a good one, with one small excepton (or perhaps one wide misconception).  What people commonly refer to as the complex plane is an unfortunate misnomer.  It should be called the "complex number plane". By calling it the complex plane (which, by the way, is a quite widespread phenomenon), one is led to think of it as being C^2.  It is not.  It is actually the real plane R^2 used as a device to represent the complex numbers C (= C^1).  Thus I would maintain (in support of Anon) that the best way to understand the hyperbolic sine and cosine functions is via restriction of the analytic continuation of the real sin and cosine functions to the imaginary number line of the complex number plane.  In a sense. the analytic continuation of the real exponential function does both for the price of one. 
One more thing, regarding your (over)reaction to Edgar's comment. Being a trained mathematician is vastly beyond taking courses in which you would first encounter hyperbolic trig functions.  If you are a major in the hard sciences or in engineering, you will be exposed to them in the near future.  I think that was Edgar's intended message, nothing more.