Notes on using PolarGraphs.xls
This workbook helps to explore the relationship between the Polar graph of r as a function of θ and the Cartesian graph of r plotted against θ . We are perhaps more familiar with the Cartesian graph and can use it as a tool to help as identify features of the Polar graph. We can for instance see where r is a maximum or minimum; find the values for which r is zero and see that they correspond to tangents at the pole; identify the symmetries of the Cartesian graph and see how they correspond to symmetries of the Polar graph.
Once you have got the idea try hiding the Polar graph and seeing if you can figure it out from the Cartesian.
There are a number of preset functions available using the drop down option box or you can enter your own being careful to include a * for multiplication. Use "q" where you would put θ and it will be automatically formated.
I have attempted to devise a system of autoscaling the graphs which seems to work well at least for fairly standard graphs.