The Desmos graphing calculator has to be one of my favourite graphing tools. It’s powerful, easy to use, allows one to share graphs and it is possible to create an account and save graphs.
Using the sliders feature students could investigate any graphs. The Further Mathematicians could easily explore the family of rose curves for example. Click on the image below then play with the sliders!
For further applets and resources to explore polar curves see this page on Mathematics Calculators.