Answer
$$\left( {\frac{1}{4},\frac{{\sqrt 3 }}{4},8} \right)$$
Work Step by Step
$$\eqalign{
& {\text{We have the cylindrical coordinates }}\left( { - 0.5,\frac{{4\pi }}{3},8} \right) \cr
& \left( {r,\theta ,z} \right):{\text{ }}\left( { - 0.5,\frac{{4\pi }}{3},8} \right) \to r = - 0.5,{\text{ }}\theta = \frac{{4\pi }}{3},{\text{ }}z = 8 \cr
& {\text{Cylindrical to rectangular}} \cr
& x = r\cos \theta \to x = - 0.5\cos \left( {\frac{{4\pi }}{3}} \right) = \frac{1}{4} \cr
& y = r\sin \theta \to y = - 0.5\sin \left( {\frac{{4\pi }}{3}} \right) = \frac{{\sqrt 3 }}{4} \cr
& z = z \to z = 8 \cr
& {\text{The rectangular coordinates are:}} \cr
& \left( {\frac{1}{4},\frac{{\sqrt 3 }}{4},8} \right) \cr} $$
