Examples

Converting to polar: pi-correction

Compute the polar coordinates of and of .

Solution

For we observe first that it lies in Quadrant II.

Next compute:

This angle is in Quadrant IV. We add to get the polar angle in Quadrant II:

The radius is of course since this point lies on the unit circle. Therefore polar coordinates are .

For we observe first that it lies in Quadrant IV. (No extra needed.)

Next compute:

So the point in polar is .

Shifted circle in polar

For example, let’s convert a shifted circle to polar. Say we have the Cartesian equation:

Then to find the polar we substitute and and simplify:

So this shifted circle is the polar graph of the polar function .