Here we give some plots of polar functions. One can do these by hand by plugging in points and using various symmetries, or one can use a calculator. Clearly we choose to use SAGE instead.

The following is a rose with 4 petals and maximum radius of 3. The 2 is controlling the number of leaves.

This is what happens when we change the 2 to a 5.

And if we change the 2 to a 4..

Here are some examples of limacons.



The next graph is of a lemniscate. The polar equation for the one graphed is $r^2 = 2 \cos(2 \theta)$, but it is easier to graph it in this case using an implicit plot and rectangular coordinates.

