Answer
$$\left( {3.0516,0.96007} \right){\text{ and }}\left( { - 3.0516,4.10166} \right)$$
Work Step by Step
$$\eqalign{
& {\text{We have the rectangular coordinates }}\left( {x,y} \right) = \left( {\frac{7}{4},\frac{5}{2}} \right) \cr
& {\text{The polar coordinates are:}} \cr
& r = \sqrt {{x^2} + {y^2}} \cr
& r = \sqrt {{{\left( {\frac{7}{4}} \right)}^2} + {{\left( {\frac{5}{2}} \right)}^2}} \cr
& r = \frac{{\sqrt {149} }}{4} \approx 3.0516 \cr
& \tan \theta = \frac{{5/2}}{{7/4}} \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{10}}{7}} \right) \approx 0.96007 \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{10}}{7}} \right) + \pi = 4.10166 \cr
& {\text{Therefore, the polar coordinates are:}} \cr
& \left( {3.0516,0.96007} \right){\text{ and }}\left( { - 3.0516,4.10166} \right) \cr} $$
