OK, i think I'm almost there,
I have the x'cosθ term, and I know I need to minus the purple section, which I trust is y'sinθ -- but I can't seem to show that it is, lol, it's the last stumbling block
I'm trying to prove that the circle is symmetrical by showing that x² + y² = a² holds when the circle rotates.
I know that this is proved given the following two formulae:
x = x'cosθ - y'sinθ
y = x'sinθ + y'cosθ
but I don't...