First let there be an arbitrary radius r.
By the arc length formula, $$r\theta=s$$
Now consider the pythagorean theorem.
so, by the sin^2+cos^2=1 identity,
Simplifying, this is actually just a true statement. The closest we can get to a solution is thus the previous finding:
This can be used to solve s in terms of x and y, but you need infinite series to solve for x in terms of y and s.