Write the equations for two limacons (and if possible graph), (one sine and one cosine) with the same a and b values. (A does not have to equal b). You may choose to use cardioids or inner loop, dimpled, or convex limacons.

Answer 1

Why not use Google to find out what a limacon looks like?
This will lead you to properties and equations of such curves.

Answer 2

you might want to play around on wolframalpha.com by varying the parameters. You have the equations for sample curves, as well as examples in your book and online.

You know the general form is r = b + a cos?. And of course, since sin? = cos(?/2 - ?) the two are just rotations of each other.

For example,

http://www.wolframalpha.com/input/?i=r+%3D+2%2B3cos%CE%B8