The Distance Formula in Polar Coordinates.
(a) Use the Law of Cosines to prove that the distance between the polar points $\left(r_{1}, \theta_{1}\right)$ and $\left(r_{2}, \theta_{2}\right)$ is
$d=\sqrt{r_{1}^{2}+r_{2}^{2}-2 r_{1} r_{2} \cos \left(\theta_{2}-\theta_{1}\right)}$
(b) Find the distance between the points whose polar coordinates are $(3,3 \pi / 4)$ and $(1,7 \pi / 6),$ using the formula from part (a).
(c) Now convert the points in part (b) to rectangular coordinates. Find the distance between them using the usual Distance Formula. Do you get the same answer?