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

Mar 14, 2015

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:
$x = r \cos \left(\theta\right)$
$y = r \sin \left(\theta\right)$

For example:
in the first one: $r = a \sin \left(\theta\right)$ choose various values of the angle $\theta$ evaluate the corresponding $r$ and plug them into the transformation equations for $x \mathmr{and} y$. Try it with a program such as Excel... it is fun!!!