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_{1}and an end angle θ

_{2}(with θ

_{2}≥ θ

_{1}and Δθ = θ

_{2}- θ

_{2}≤ 2π). The total distance traveled is equal to the arc length of the segment: L = R(Δθ).

I would like to find the distance covered by the particle along the X axis and the distance covered by the particle along the Y axis.

I'm not sure how to do this unless I break up the arc at each quadrant crossing and analyze the pieces separately.

Any tips are greatly appreciated.