Desmos is so lovely. Unlike GeoGebra, which is great, too, it can graph polar things!

It is super user-friendly: to get theta you can click the button for it, or you can just type “theta” and it knows what you mean. It is very easy to edit and delete functions. Making a slider is as easy as typing a non-variable letter and just clicking on it. Idea that I’m having too late: type in r = 2 + bsin(theta) and drag the slider to show how cardioids and limaçons and the loopy ones are related!

I had the students do an investigation about polar graphs in pairs. Last year I gave them some work ahead of time about what polar coordinates were, but I decided to postpone that this time. I thought it might be better to let them discover more on their own.

I’m attaching my PDFs, but mainly I just gave them a good amount of each type of equations and asked them to sort and then to generalize.

I cut these functions out and put them in an envelope: polar task chart and functions

These are the instructions: polar task

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