Ah, I see! I was able to get a version of it working just by using the x_1 and y_1 as the theta and r variables directly (without computation of a theta_1). I have it on slide 2 of a copy of your activity:
You also might be interested in the activity talked about in this post Side by Side Graphs Polar/Rectangular which also does some interesting things with cartesian to polar coordinates!
If you just want to look at what I did on the graphs, this is the cartesian graph:
and the polar graph: