What are the polar coordinates of the rectangular coordinates (2,−2√ 3)

Rectangular  coordinates =  ( r*cos ( theta) , r * sin  (theta))

a)   ( 4 cos 5pi/3, 4sin5pi/3)  =  ( 4cos300°, 4sin 300°) =  4 (1/2) , 4 (-sqrt (3)/2) )  = ( 2, - 2 sqrt (3) )

b)  (2, 11pi/6)  =  ( 2 cos 330 , 2 sin 330)  =  ( 2sqrt (3) /2  ,  2 (-1/2) ) =  (sqrt (3) ,- 1)

You should be able to  finish the last two.....let me  know if you get  stuck

Find    'r' via pythag theorem

2^2 + (-2 sqrt3)^2 = r^2

r = 4             so answer A or B are possibles

   find angle   arctan (-2sqrt3 /2)  = -60 degrees   or  5pi/3           Do you see how to do it?