OH ok we're talkin' about the angle of rotation...delta angle... which is a constant... not the total angle.
x is always going to be R*cos(angle) but if we're going from x to x' then it's
the derivative of Rcos(angle) which is cos(angle)^2-Rsin(angle)^2
R*cos(angle)*cos(angle) - R*sin(angle)*sin(angle)
substituting since y=r*sin(angle) we can substitute and get
R*cos(angle)*cos(angle) -y*sin(angle)
and since x = cos(angle) [I'm taking baby steps here]
we can substitute more
x*cos(angle)-y*sin(angle)
BOOM!