Yes, but do you really need to scale all your values to make the rotation amount fit into a sin() call, only to have to scale them back again when you're done?

I think what they're getting at is "why are we scaling everything so one full turn is sin(6.28ish) when we can just say sin(1)?"

You could easily try it out by defining a function that replaces sin(), cos(), and tan() with their "turn" equivalents, and seeing how you get on.

Euler angles have nothing to do with e^ix = cos x + i sin x. They are a completely different concept.

I am very familiar :) using euler angles involves using trig functions, which is what this thread is about

Yes and no. The x in e^ix is to SO(2) what Euler angles are to SO(3).

This really only says that the connection between Euler's formula and Euler angles is that they're both angles. I would agree with that.

One represents rotation in 2D space, the other in 3D. So I think it's a bit more than that.