But why?

See, I was taught this, but no one could every answer why sine and cosine worked the way they did.

This definition just explains how they work with triangles. What's the actual definition of each, and how was that derived? I can apply them all day long yet I still can't tell you what either one means.

I had the same issues with different kinds of equations, no one ever explained why you'd do a certain thing in a given step (e.g. Quadratic) even when I asked, repeatedly. The answer was always "you just do". Well that doesn't help with knowing when to apply a rule.

And that was my experience with any math, right through college (3 universities). Most teachers suck, but holy shit math teachers are down right moronic. They can't understand why students don't get it. Well, try actually teaching something for a fucking change.