How exactly does one calculate trigonometric functions without a calculator. I recognize the whole Sohcahtoa thing, that is not what I am talking about. I am referring to when we are given something like sin(a), how exactly would this actually be calculated. I can't find any answers, it is just expected that people use calculators for it.
I know you don't need the sides of a triangle to even do it, as shown by how you can just place sin(x) into a calculator. But I was only ever taught how to do things in reference to triangles, and to use the calculator for it. Except when we were expected to do it without a calculator but with never being once taught how to do it without one.