Graph $r=\cot(\theta)\csc(\theta)$. So I am stuck on a graphing question in polar coordinates.  I am not sure how to graph the equation even after writing down a few points:
$\cot(0)\csc(0) $DNE
$\cot(\dfrac {\pi}{4})\csc(\dfrac {\pi}{4})= \sqrt{2}$,
$\cot(\dfrac {\pi}{2})\csc(\dfrac {\pi}{2})= 0,$
$\cot(\dfrac {3\pi}{4})\csc(\dfrac {3\pi}{4})= -\sqrt{2}$,
$\cot(\pi)\csc(\pi) $DNE,
and so on.  
Obviously I can just graph it online, but can someone explain the mechanics to how to graph it without using a graphing calculator or desmos?  Thanks!

It might help to convert the equation to rectangular form using the identities


*

*$x=r\cos\theta$

*$y=r\sin\theta$
\begin{eqnarray}
r&=&\cot\theta\csc\theta\\
r&=&\frac{\cos\theta}{\sin^2\theta}\\
r\sin^2\theta&=&\cos\theta\\
r^2\sin^2\theta&=&r\cos\theta\\
y^2&=&x
\end{eqnarray}
ADDENDUM: Note that multiplying both sides by $r$ introduces an extraneous solution at the origin.
ADDENDUM-2: As Oscar Lanzi points out, there is a value of $\theta$ which includes the origin, so the origin is NOT an extraneous solution.
