Answer
(a) See the graph.
(b) Quadrant I
(c) $\frac{\pi}{3}$ and $-\frac{5\pi}{3}$
Work Step by Step
(b) A positive coterminal angle of $-\frac{4\pi}{3}$ is $\frac{2\pi}{3}$
$0\lt\frac{\pi}{3}\lt\frac{\pi}{2}$, therefore, it lies in quadrant I.
(c)
$-\frac{23\pi}{3}+3(2\pi)=-\frac{5\pi}{3}$
$-\frac{23\pi}{3}+4(2\pi)=\frac{\pi}{3}$
