Answer
See graph below.
Work Step by Step
The question ONLY asks for a graph of the polar equation. It asks for a graphing device to graph the polar equation.
For the domain, $0 \leq θ \leq 4\pi$
Given $r = \cos \frac{θ}{2}$
See the graph below.
If the domain is set to $2\pi$, then only half the graph will be present, so the domain is set to $4\pi$