Answer
$a.\quad (1,1)$
$b.\quad (0, 1)$
$c.\quad (-\sqrt{3},1)$
Work Step by Step
Polar coordinates $(r,\theta)$
Cartesian coordinates:$ \quad(r\cos\theta,r\sin\theta)$
$a.$
Plot point A:
r is negative, terminal side is $\displaystyle \frac{5\pi}{4}$+$\displaystyle \pi=\frac{9\pi}{4}$
($ \pi/$4 $above$ the +x axis, at distance $\sqrt{2}$)
Cartesian coordinates:$\quad $
$(-\displaystyle \sqrt{2}\cos\frac{5\pi}{4},-\sqrt{2}\sin\frac{5\pi}{4})= (-\displaystyle \sqrt{2}(-\frac{\sqrt{2}}{2}),-\sqrt{2}(-\frac{\sqrt{2}}{2}))=(1, 1)$.
$b.$
Plot point B:
r is positive, terminal side: $5\pi/2$
($ \pi/2$ above the +x axis, at distance 1)
Cartesian coordinates:$\quad $
$(1\displaystyle \cos\frac{5\pi}{2},1\sin\frac{5\pi}{2})=(0, 1).$
$c.$
Plot point C:
r is positive, terminal side: $-7\pi/6$
($ \pi/6$ above the -x axis, at distance 2)
Cartesian coordinates:$\quad $
$(2\displaystyle \cos(-\frac{7\pi}{6}),2\sin(-\frac{7\pi}{6}))= (2(-\displaystyle \frac{\sqrt{3}}{2}),2(\frac{1}{2}))=(-\sqrt{3},1)$
