Answer
$P$ = (-3$\sqrt3$,3)
Work Step by Step
The Point $P$ is represented by the coordinate ($x$,$y$).
$\cos$ $\theta$ = $\frac{x}{r}$
$\cos$ 150$^{\circ}$ = $\frac{x}{6}$
x = 6 $\cos$ 150$^{\circ}$
x = 6(-$\frac{\sqrt3}{2}$)
x = -3$\sqrt3$
$\sin$ $\theta$ = $\frac{y}{r}$
$\sin$ 150$^{\circ}$ = $\frac{y}{6}$
y = 6 $\sin$ 150$^{\circ}$
y = 6($\frac{1}{2}$)
y = 3
Therefore:
$P$ = (-3$\sqrt3$,3)
