Help on hyperbolic functions

Even after taking calculus, I've not learned hyperbolic functions, which leads me to believe that it's a relatively minor part of mathematics. Nevertheless, I want to learn them. Now, after googling for a while, I've gotten a general idea of what hyperbolic functions stand for but I still need some clarification.

(1.)Let's take sinh(x). Does "x" represent angle, either degree or radian? Or something else?

(2.) Why does the graph of sinh(x) go to infinity if it doesn't even reach one (to my limited knowledge, of course). I mean, if you look at the unit hyperbola and use the trig sin, you'll see that the sine ratio never exceeds 1. I'm sure I'm missing something here.

(3.) What is the general domain of hyperbolic functions? I mean, for standard trig, it's nonexistent (because it'll go in circles) but what about hyperbolic functions? It's difficult to visualize the domain for a split-up graph like a hyperbola.

etc., etc., etc... I'd just appreciate some solid instruction regarding hyperbolic functions. They're not found in my textbook and the internet sucks at clarification.

I wasn't sure if this calculus section was the appropriate place to post because I don't know where hyperbolic functions belong. I'm sorry if it doesn't belong to this calculus section.