You need to convert the cartesian coordinates to polar: This means we need to go from (x, y) --> (r, angle)
We can covert, using the following formulas:
Find r:
[tex](x, y) --> (2, 2\sqrt{3})[/tex]
[tex]r^2 = \sqrt{x^2 + y^2} [/tex]
[tex]r^2 = \sqrt{2^2 + (2\sqrt{3})^2}[/tex]
r = 4
Now, find our angle:
Use the inverse of tan
[tex]\tan^{-1} \frac{2}{2\sqrt{3}} = 30\deg [/tex]
Turn 30 degrees to radian
[tex]\frac{\pi}{180} * 30 = \frac{1}{6}\pi[/tex]
Answer = [tex](4, \frac{1}{6}\pi)[/tex] = C
