# Chapter 6 - Section 6.4 - Graphs of Polar Equations - Exercise Set - Page 755: 78

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.

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