File:Cartesian to polar.gif

English: A function in the Cartesian plane can be transformed into polar coordinates by wrapping one axis around itself and collapsing it to a point. This is illustrated here transforming the Cartesian graph ${\displaystyle y=\sin(6x)+2}$ into the polar graph ${\displaystyle r=\sin(6\theta )+2}$.

The general transformation takes the following steps:

1. Start with Cartesian graph.

2. Clip the graph to satisfy ${\displaystyle y>0}$ (not necessary in the example ${\displaystyle y=\sin(6x)+2}$).

2. Reflect in the line ${\displaystyle y=x}$.

3. Bend it to backwards on itself, as shown in the animation, to obtain the polar graph.