$$ \huge \frac{r}{ \sin(\theta) } = 10 - \tan(\theta) $$

PolarPlot[
	If[
		Sin[theta] (10 - Tan[theta]) > 0, 
		Sin[theta] (10 - Tan[theta])
	],
	{theta, 0, 2 Pi},
	PlotRange  -> {{-8, 8}, {-8, 8}},
	FrameTicks -> None,
	     Axes  -> None,
	     Frame -> True
]