Plot the points with polar coordinates (-6,-(11pi )/(6)) and (3,(pi )/(3)) using the pencil.

To plot the points with polar coordinates $(-6,-\frac {11\pi }{6})$ and $(3,\frac {\pi }{3})$, we need to convert them to Cartesian coordinates.<br /><br />For the point $(-6,-\frac {11\pi }{6})$:<br />$x = -6 \cdot \cos(-\frac {11\pi }{6}) = -6 \cdot \cos(\frac {5\pi }{6}) = -6 \cdot (-\frac {\sqrt{3}}{2}) = 3\sqrt{3}$<br />$y = -6 \cdot \sin(-\frac {11\pi }{6}) = -6 \cdot \sin(\frac {5\pi }{6}) = -6 \cdot (\frac {1}{2}) = -3$<br /><br />For the point $(3,\frac {\pi }{3})$:<br />$x = 3 \cdot \cos(\frac {\pi }{3}) = 3 \cdot \frac {1}{2} = \frac {3}{2}$<br />$y = 3 \cdot \sin(\frac {\pi }{3}) = 3 \cdot \frac {\sqrt{3}}{2} = \frac {3\sqrt{3}}{2}$<br /><br />So, the Cartesian coordinates for the points are:<br />$(-6,-\frac {11\pi }{6}) \rightarrow (3\sqrt{3}, -3)$<br />$(3,\frac {\pi }{3}) \rightarrow (\frac {3}{2}, \frac {3\sqrt{3}}{2})$<br /><br />Now, we can plot these points on the Cartesian coordinate system.