Let $r_1 = 2 + \cos(θ)$, $r_2 = 2 + 2\cos(θ)$, and $r_3 = 2 + 3\cos(θ)$. .

1. What are the minimum values of $r$ for each of the functions? What are the corresponding $θ$-values?

   Hint (a):

   Recall that $–1 ≤ \cos(θ) ≤ 1$.

2. How does your answer to part (a) explain what happens to the graphs as $θ$ moves from $\frac { \pi } { 2 }$ to $\frac { 3 \pi } { 2 }$ ?

   Hint (b):