## Calculus (3rd Edition)

1. First find the points $A$ - $G$ in polar coordinates for $\theta = 0,\frac{\pi }{6},\frac{\pi }{3},...\pi$. 2. Then, plot the points $A$ - $G$ in polar coordinates and sketch the curve by joining them.
Using the method in Example 9, we obtain points $A$ - $G$ in polar coordinates for $\theta = 0,\frac{\pi }{6},\frac{\pi }{3},...\pi$ and list them on a table: $\begin{array}{*{20}{c}} {}\\ \theta \\ {r = 3\cos \theta - 1} \end{array}\begin{array}{*{20}{c}} A\\ 0\\ 2 \end{array}\begin{array}{*{20}{c}} B\\ {\frac{\pi }{6}}\\ {\frac{{3\sqrt 3 }}{2} - 1} \end{array}\begin{array}{*{20}{c}} C\\ {\frac{\pi }{3}}\\ {\frac{1}{2}} \end{array}\begin{array}{*{20}{c}} D\\ {\frac{\pi }{2}}\\ { - 1} \end{array}\begin{array}{*{20}{c}} E\\ {\frac{{2\pi }}{3}}\\ { - \frac{5}{2}} \end{array}\begin{array}{*{20}{c}} F\\ {\frac{{5\pi }}{6}}\\ { - \frac{{3\sqrt 3 }}{2} - 1} \end{array}\begin{array}{*{20}{c}} G\\ \pi \\ { - 4} \end{array}$ Then we plot the points $A$ - $G$ in polar coordinates and sketch the curve by joining them.