Polar Co-ordinates

Fix a point $O$ in a plane, called the pole, and a fixed ray $OX$ starting at $O$, called the polar axis. For any point $P$ in the plane other than $O$, let $r=OP$ (the length of the segment joining $O$ and $P$) and let $\theta=m\angle XOP$ (the angle the ray $OP$ makes with the polar axis $OX$). The ordered pair $(r,\theta)$ completely determines the position of $P$ and is called its polar co-ordinates: $r$ is the radius vector and $\theta$ is the vectorial angle of $P$.

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