Polar Coordinates

This is a Helper Page for:
Change of Coordinate Systems
Harmonic Warping

Polar Coordinates are coordinates which locate points by their distance from the origin and their rotation from the positive x-axis. Traditionally, $r$ represents distance from the origin and $\theta$ represents rotation in radians from the positive x-axis.

For example, the point $(x,y) = \left (\tfrac{1}{\sqrt{2}},\tfrac{1}{\sqrt{2}} \right )$ is 1 unit from the origin (as can be seen by the Pythagorean Theorem) and is a rotation of $\tfrac{\pi}{4}$ from the positive x-axis, so can be represented in polar form by: $(r,\theta)= \left (1,\tfrac{\pi}{4} \right )$.

Locating a point using its distance from the origin and its rotation for the + x-axis