Investigate the family of curves given by r = a + b cos(n( + )) where a,

Question:

Investigate the family of curves given by r = a + b cos(n(θ + ϕ)) where a, b, and ϕ are real numbers and n is a positive integer. As you answer the following questions, be sure that you graph a sufficient number of examples to justify your conclusions.
a. How are the graphs for ϕ = 0 related to those for which ϕ ≠ 0?
b. How does the graph change as n increases?
c. How do the relative magnitude and sign of a and b change the nature of the graph?