Question

convert r(θ)=2/(2cos(θ)+3sin(θ)) to a cartesian function

Answer 1

you have the following equations to use:
\[x=rcos(\theta)\]
\[y=rsin(\theta)\]
\[x^2+y^2=r^2\]
\[\tan(\theta)=\frac{y}{x}\]

Answer 2

do you might want to try moving the cos sin part with the r part to try to use those first two equation