Question

What is the general form of limacons and cardioids and how do you graph transformations?

Answer 1

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:
`x=rcos(theta)`
`y=rsin(theta)`

For example:
in the first one: `r=asin(theta)` choose various values of the angle `theta` 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!!!