Answer
$$\left( { - \frac{1}{2},\frac{{\sqrt 3 }}{2}} \right)$$
Work Step by Step
$$\eqalign{
& \left( {1,\frac{{2\pi }}{3}} \right) \Rightarrow r = 1{\text{ and }}\theta = \frac{{2\pi }}{3} \cr
& {\text{Converting to cartesian coordinates }}\left( {x,y} \right).{\text{ Where}} \cr
& x = r\cos \theta {\text{ and }}y = r\sin \theta \cr
& {\text{We obtain}}{\text{,}} \cr
& x = 1\cos \left( {\frac{{2\pi }}{3}} \right) = - \frac{1}{2} \cr
& y = 1\sin \left( {\frac{{2\pi }}{3}} \right) = \frac{{\sqrt 3 }}{2} \cr
& {\text{The cartesian coordinates are:}} \cr
& \left( {x,y} \right) = \left( { - \frac{1}{2},\frac{{\sqrt 3 }}{2}} \right) \cr} $$
