How to write $x=2\cos(3t) y=3\sin(2t)$ in rectangular coordinates? How would I write the following in terms of $x$ and $y$? I think I use the inverse $\cos$ or $\sin$?
$$x=2\cos(3t)\,, \quad y=3\sin(2t)$$

Hint:
$$ x=2\cos(3t) =  2\cos(2t+t)= 2\cos (2t)\, \cos t - 2 \sin (2t) \,\sin t $$

$$ \implies x = 2\cos (2t)\, \cos t - 2 \sin (2t) \,\sin t\longrightarrow (*). $$

Added: To finish the problem you need to find $\cos(2t),\sin t$, and $\cos t$ in $(*)$. For $\cos (2t)$ we have 
$$ \sin(2t)=\frac{y}{3}\implies  \cos (2t) = \sqrt{1-\sin^2(2t)}= \sqrt{1-\frac{y^2}{9}}. $$
For $\cos t$ and $\sin t$, use the identities

$$ \cos(2t)=2\cos^2 t-1,\quad \cos(2t)=1-2\sin^2 t. $$

