Question

What does a polar coordinate system look like?

Answer 1

A polar coordinate system consists of a polar axis, or a "pole", and an angle, typically `theta`. In a polar coordinate system, you go a certain distance `r` horizontally from the origin on the polar axis, and then shift that `r` an angle `theta` counterclockwise from that axis.

This might be difficult to visualize based on words, so here is a picture (with O being the origin):

This is a more detailed picture, depicting a whole polar coordinate plane (with the `theta`'s in radians):

The origin is in the middle, and each circle represents a different `r` (which is actually a radius). If you follow the line of that given circle with radius `r` along the angle, you can get polar coordinate points in the form `(r,theta)`

Note that polar coordinates/equations have Cartesian equivalents shown below: