I took Pre-Calculus in a 90-minute block for one semester and the format was predictable: 40-50 minutes of lecture on two textbook sections then we got to start our homework. Towards the end we learned about the trippy world of polar equations and rose curves. It's the one thing I really remember (except mathematical induction which can burn in a fire). We learned some general properties and sketched them by hand. Everyone had a TI-83 or some sort, but I'm not sure we ever learned how to plot them on there. We fiddled with the subject briefly and then it was gone.
Twelve years later and the conventional tools available have not changed. Maybe you have TI-84s instead of TI-83s. Think about the cell phone you (did not) have twelve years ago.
This isn't a total indictment on TI. Their N-spire products seek to improve the quality of graphing input. The standalone calculators are expensive but the N-spire software for the iPad is $30 (it was even for sale for $5 at launch). That's something.
But presented for examination, various ways to graph r = 4 cos 3 theta:
TI-89 Titanium - $175.00
GraphCalc HD - $1.99 (iPhone version)
Desmos.com - Free
And this ignores the setup process. Do I have to explicitly set polar mode? radians? theta step? wait, what? how do I trace? Mister, where's my graph? uh, what do you mean window? Shouldn't we have reached a point in the last twelve years that the tools most students can access will accomplish something without making them answer so many questions?
In case you can't tell where I stand, the TI-84s stayed in the buckets the entire time we explored polar equations.