I am trying to parameterize the following implicit equation so that I can sketch it.
$x^2+y^2=1+4.5\sin^2(xy)$
However, I am having problems with parameterizing the equation because of the $xy$ and inside the sine function.
The usual way would be to use the trigonometric identity $sin^2(x)+cos^2(x)=1$ when trying to parameterize a equation. For example if we would parameterize $x^2+y^2=1$. Then I would just put $x=rcos(\theta)$ and that would give me $y=rsin(\theta)$.
I have tried to put $x=arcsin^2(t)$ to get rid of the sine function and then solve for $y$. However, I dont get the answer that I want to be able to sketch it.
How would one approach this equation to find an appropriate parameterization?