I'm a little over half way through calculus 1 at my local community college. We are currently covering hyperbolic functions. Ex. sinh, cosh.. etc. The text book, and the professor have taught us that for sinh and cosh they are actually just aliases for the more specific functions. and .

I find knowing the exact functions which they represent to be very helpful in working with and understanding these functions. My question is, do the trig and functions have actual numeric functions which they translate to like the hyperbolic functions do? I understand that and represent the y and x points respectively, but It would be very helpful if they also were shorthand for other more sensible functions like the hyperbolic functions are.