A Look at Three Polar Equations

by Amy Benson


The first equation we graph is

To see the steps to rewrite this polar equation in rectangular form, click here.


The second equation of interest at this moment is

We expect from the equation that the first equation is the parent of this one and that the graph will reflect this relationship.

Indeed, the new graph closely resembles the first graph. The difference between the graphs being that this one is rotated 45 degrees counterclockwise about the origin, as seen here (red = original).

To view further rotations of the original graph, click here.

The final equation we will investigate is

Let's see what happens when we change individual signs within the equation. Click here.