Ok so i feel a little silly for never having learned this.

So i understand what lots of common functions do. For example, i understand that e^1 is somewhere around 2.7-something, sin90=0, natural log of 2 is about .7 and so on and so on.

I guess what I'm wanting to know is how exactly these functions are what they are. WHY does e=2.7? Where does that number come from? Same thing for log and natural log functions. What do the trig functions represent (note: I'm NOT looking for the answer "They represent an oscillating curve", or "It's the opposite over hypotenuse on a right triangle". I want to know more than that. Think about it like, when you enter "tan(67)" on a calculator, what exactly is it calculating?)

At least in Calc 1,2, and 3 there were explanations of what exactly everything meant and their theories. But i never understood these basic functions that I use almost every day.