Problem:
Given the family of parametric equations

x = (a + cos(3t)) cos(t)
and
y = (a + cos(3t)) sin(t)

with parameter a, draw the graphs for various values of a between -2 and 2.


Visualization:
The following LiveMath notebook contains an animation which draws the desired graphs as a ranges from -2 to 2 in steps of 0.2. In addition, you can change the values of the constants in the equations and see the effect on the graph. View an animation to see how this can be done.