Hi jeff,
From 1971 to 1986, I used trig everyday. (back in my manual drafting days) Now I only use it occasionally to double-check some things. Ever since we started CAD, I've been letting the computer do the work of figuring out the math. And since it does a pretty good job, I have practically forgotten how to do trig. For sure I forgot how to spell it.
So to your question, no you do not have to do the math, but you still have to know something, ie; the base diameter and height and it'll do the rest.
Play around with the solid cone a bit. You'll get the hang of it.
P.S. If you know the base diameter and the the taper angle, just draw it in 2D to find the height, then do the cone command.