I am not a skilled mathematician,

I can usually grind my way through to the answer after great effort,

which is why I didn't check your initial answer in the initial post.

However I was surprised to see that you got __identical__ answers for X and Y

For circular motion (in general) I would expect to see very __similar__ solutions for X and Y,

But I would expect one to be 90degrees out of phase with the other.

Is this one of those situations where there are multiple possible solutions,

possibly at 90 degree phase intervals (pure guess)

My suspicion is that your solutions __are correct__, just not the appropriate ones.

(like the multiple roots of a polynomial, which do you choose).