#### Answer

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.

#### Work Step by Step

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.