Polar coordinates

A point located by distance $r$ from the origin and angle $\theta$ from the positive $x$ -axis, instead of $(x,y)$ .

Polar coordinates $(r,\theta)$ locate a point by its distance $r$ from the pole (origin) and the angle $\theta$ measured counterclockwise from the positive $x$ -axis, converting to rectangular via $x=r\cos\theta$ , $y=r\sin\theta$ . Unlike rectangular coordinates, a single point has INFINITELY many polar representations (adding $2\pi$ to $\theta$ , or negating $r$ and adding $\pi$ to $\theta$ , gives the same point).

Examples

$(r,\theta)=(2,\pi/2)$ is the same point as rectangular $(0,2)$ .
$(2,\pi/2)$ , $(2,\pi/2+2\pi)$ , and $(-2,3\pi/2)$ all name the same point.