Image: Cartesian to polar
Description: 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 y=sin(6x)+2{\displaystyle y=\sin(6x)+2} into the polar graph r=sin(6θ)+2{\displaystyle r=\sin(6\theta )+2}. The general transformation takes the following steps: 1. Start with Cartesian graph. 2. Clip the graph to satisfy y>0{\displaystyle y>0} (not necessary in the example y=sin(6x)+2{\displaystyle y=\sin(6x)+2}). 2. Reflect in the line y=x{\displaystyle y=x}. 3. Bend it to backwards on itself, as shown in the animation, to obtain the polar graph.
Title: Cartesian to polar
Credit: Own work
Author: Kieff
Usage Terms: Public domain
License: Public domain
Attribution Required?: No
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