Answer
$$\left( {5,2.214} \right){\text{ and }}\left( { - 5,5.3558} \right)$$
Work Step by Step
$$\eqalign{
& {\text{We have the rectangular coordinates }}\left( {x,y} \right) = \left( { - 3,4} \right) \cr
& {\text{The polar coordinates are:}} \cr
& r = \pm \sqrt {{x^2} + {y^2}} \cr
& r = \pm \sqrt {{{\left( { - 3} \right)}^2} + {{\left( 4 \right)}^2}} \cr
& r = \pm 5 \cr
& \tan \theta = \frac{4}{{ - 3}} \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{4}{{ - 3}}} \right) + 2\pi \approx 5.3558 \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{4}{{ - 3}}} \right) + \pi \approx 2.214 \cr
& {\text{Therefore, the polar coordinates are:}} \cr
& \left( {5,2.214} \right){\text{ and }}\left( { - 5,5.3558} \right) \cr} $$
