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