how to convert v(theta,r)=r^2*sin(1.5*theta)^2 to Cartesian coordinates? please help

Question

anonymous · Answer

$$r^2=x^2+y^2\
x=r\cos\theta\
\color{red}{y=r\sin\theta}$$
I think the red equation would help the most here. Remember to adjust for the 1.5$\theta$

anonymous · Answer

that is what i don't know how to do. would it be just v(x,y)=(x^2+y^2)(sin(1.5*arctan(y/x))^2? because the graph of that is not the same as the graph of v(theta, r) in polar coordinates.

anonymous · Answer

Let's back up a bit. This problem seems a bit more complicated than I expected. It is
$$v(\theta,r)=r^2\sin^2\left(\frac{3}{2}~\theta\right),~\text{ right?}$$

anonymous · Answer

i did get it. you needed to convert the expreasion into aall sins and cos in order to do it. thanks anyways