Answer
$$\left( {2,120^\circ } \right)$$
Work Step by Step
$$\eqalign{
& {\text{Let the rectangular coordinates }}\left( { - 1,\sqrt 3 } \right){\text{ }} \cr
& x = - 1{\text{ and }}y = \sqrt 3 \cr
& \cr
& {\text{Convert to polar coordinates }}\left( {r,\theta } \right) \cr
& r = \sqrt {{x^2} + {y^2}} \cr
& r = \sqrt {{{\left( { - 1} \right)}^2} + {{\left( {\sqrt 3 } \right)}^2}} \cr
& r = 2 \cr
& and \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{y}{x}} \right) \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{\sqrt 3 }}{{ - 1}}} \right) + 180^\circ \cr
& \theta = 120^\circ \cr
& \cr
& {\text{The polar coordinates are:}} \cr
& \left( {2,120^\circ } \right) \cr} $$
