Chapter 12.1, Problem 98E

Beautiful curves Consider the family of curves

$\begin{array}{l}x=\left(2+\frac{1}{2}\sin at\right)\cos \left(t+\frac{\sin bt}{c}\right),\\ y=\left(2+\frac{1}{2}\sin at\right)\sin \left(t+\frac{\sin bt}{c}\right).\end{array}$

Plot the curve for the given values of a, b, and c with 0 ≤ t ≤ 2π. (Source: Mathematica in Action, Stan Wagon, Springer, 2010; created by Norton Starr, Amherst College)

56. a = 6, b = 12, c = 3