I have this polar equation:
$$r=4\csc\theta$$
My initial idea was to plug into the cartesian equations for $x$ and $y$, so I got:
$$x=4\csc\theta\cos\theta=4\cot\theta$$
$$y=4\csc\theta\sin\theta=4$$
But the solution says to do this:
$$r=\frac{4}{\sin\theta}$$
Multiplying both sides by $\sin\theta$ yields:
$$r\sin\theta=4$$
Since $y=r\sin\theta$, we get $y=4$.
I understand that I also got $y=4$ (which is just horizontal line) but I also got $x=4\cot\theta$.
How would I know to just not use the value that I got for $x$? The answer just says $y=4$ which is a horizontal line.