The rotating angle suggests immediately the domain and definition of Sin(x), Cos(x) using simple projections. And, huuuuge bonus, that's a right triangle.

I just think lesson zero in the above article should have been these projections, and a simple "From this all angles can be defined as right triangles in your preferred coordinate system", and you're off to the races in any old direction.

This is not how I was taught it, and I'm retrospectively upset.