I think the answer is ((4 - 2 cos(n))/(5-4 cos(n)), 2 sin(n)/(5 - 4 cos(n))
Here's how you arrive at this answer: I'll write the point (x,y) in the plane as the complex number x + i y. We'll use Euler's formula, e^(it) = cos(t) + i sin(t).
The distance you travel in the kth step is...