Answer
$r = 2~sin~\theta~tan~\theta$
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Work Step by Step
$r = 2~sin~\theta~tan~\theta$
When $\theta = 0^{\circ}$, then $r = 2~sin~0^{\circ}~tan~0^{\circ} = 0$
When $\theta = 30^{\circ}$, then $r = 2~sin~30^{\circ}~tan~30^{\circ} = 0.58$
When $\theta = 60^{\circ}$, then $r = 2~sin~60^{\circ}~tan~60^{\circ} = 3$
When $\theta = 75^{\circ}$, then $r = 2~sin~75^{\circ}~tan~75^{\circ} = 7.2$
When $\theta = 75^{\circ}$, then $r = 2~sin~85^{\circ}~tan~85^{\circ} = 22.8$
When $\theta = 90^{\circ}$, then $r = 2~sin~90^{\circ}~tan~90^{\circ} = undefined$
When $\theta = 120^{\circ}$, then $r = 2~sin~120^{\circ}~tan~120^{\circ} = -3$
When $\theta = 180^{\circ}$, then $r = 2~sin~180^{\circ}~tan~180^{\circ} = 0$
When $\theta = 240^{\circ}$, then $r = 2~sin~240^{\circ}~tan~240^{\circ} = -3$
When $\theta = 270^{\circ}$, then $r = 2~sin~270^{\circ}~tan~270^{\circ} = undefined$
When $\theta = 300^{\circ}$, then $r = 2~sin~300^{\circ}~tan~300^{\circ} = 3$
This graph is a cissoid.
We can see this graph below:
