Challenge Level

The point $P$ with polar coordinates $(r,\theta)$ is such that $OP=r$ and the angle between the x-axis and the line through $OP$ is $\theta$ measured counter clockwise. Equivalently if $P$ has Cartesian coordinates $(x,y)$ then $x=r\cos \theta$ and $y=r\sin \theta$.

The question asks for an explanation of the features of the graph. If you want to use a software package to sketch the graph you may want to download the shareware graphing software Graphmatica .