Sketch a a polar coordinate plot of \[ r=1+2 \sin 3 \theta, 0 \leq \theta \leq 2 \pi . \]

Question

(a) Sketch a a polar coordinate plot of
\[
r=1+2 \sin 3 \theta, 0 \leq \theta \leq 2 \pi .
\]

(b) How many points lie in the intersection of the two polar graphs
\[
r=1+2 \sin 3 \theta, 0 \leq \theta \leq 2 \pi
\]
and
\[
r=1 \text { ? }
\]
(c) Algebraically find all values of \(\theta\) that
\[
1=1+2 \sin 3 \theta, 0 \leq \theta \leq 2 \pi .
\]
(d) Explain in a sentence or two why the answer to part (b) differs from (or is the same as) the number of solutions you found in part (c).