Find a Cartesian equation relating x and y corresponding to the parametric equations $x=3\sin(6t)$, $y=6\cos(6t)$.
Write your answer in the form P(x,y)=0 where P(x,y) is a polynomial in x and y such that the coefficient of $y^2$ is 9.
Attempt:
This seems a difficult problem, since we don't know how x and y are related. First, knowing the identity $\sin t=\cos(t+\frac{\pi}{2})$, I attempted the following
$$x+y=3\sin(6t)+6\sin((6+2\pi)t$$
But then, the coefficient of $y$ is 1. So trying:
$$x+9y^2=3\sin(6t)+9(6\sin((6+2\pi)t)^2$$
But from here I am stuck.
Any hints?
Thanks