Answer
(a) We can see the point plotted on the graph below.
(b) We can write two pairs of polar coordinates for this point:
$(\sqrt{3}, 60^{\circ})$
$(-\sqrt{3}, 240^{\circ})$
Work Step by Step
$(\frac{\sqrt{3}}{2}, \frac{3}{2})$
(a) We can see the point plotted on the graph below.
(b) $r = \sqrt{(\frac{\sqrt{3}}{{2}})^2+(\frac{3}{2})^2} = \sqrt{3}$
We can find the angle $\phi$ above the positive x-axis:
$tan~\phi = \frac{\frac{3}{2}}{\frac{\sqrt{3}}{2}}$
$\phi = arctan(\sqrt{3})$
$\phi = 60^{\circ}$
We can write two pairs of polar coordinates for this point:
$(\sqrt{3}, 60^{\circ})$
$(-\sqrt{3}, 240^{\circ})$
