Oh, sorry, that didn't come off quite right.

I guess it feels weird to me because unlike things like logic or group theory, trigonometry was invented for practical reasons and then made its way into theoretical mathematics. So when I think of trig I think surveying or gunnery or construction or that sort of thing, but of course it isn't obvious if you don't know.

I'll be less annoying less time!

Euler's Identity is so weird when you think about it that when I first read it as a boy, I flat out refused to admit that it was true, and thought it was some sort of joke. Now I understand it, and I think it's beautiful because it unifies rotation and exponential growth into one thing.