What is the general form of limacons and cardioids and how do you graph transformations?
You can find a lot of information and easy explained stuff in “K. A. Stroud – Engineering Mathematics. MacMillan, p. 539, 1970”, such as:
If you want to plot them in Cartesian coordinates remember the transformation:
in the first one: r=asin(θ) choose various values of the angle θ evaluate the corresponding r and plug them into the transformation equations for x and y. Try it with a program such as Excel… it is fun!!!