Answer
If $\theta \,\max =\pi $, the graph is drawn once.
Work Step by Step
From the plot we can observe that from $\theta =0\,\text{to}\,\theta \text{=}\pi $, the curve is plotted exactly once.
Beyond $\theta =\pi $, the curve retracts its path again.
Follow the steps given below in TI83 calculator:
Step 1. Open TI83 calculator.
Step 2. Select MODE. In MODE select RADIAN and POLAR form.
Step 3. Now, select Y=. Type the function in polar form ${{r}^{2}}=4\sin \left( 2\theta \right)$.
Step 4. Press WINDOW option.
Step 5. In WINDOW set range for x $\left( -4,4 \right)$. Set range for y $\left( -2.5,2.5 \right)$.
Step 6. Set the scale for x and y as 1 and $\theta \,\text{step}\,\text{=}\,\text{0}\text{.1}$.
Step 7. Press TRACE.
The above graph represents the polar equation ${{r}^{2}}=4\sin \left( 2\theta \right)$ for $\theta =\pi $.
The above graph is a lemniscate.
