Using the arctan function of the calculator, we obtain.
t = 1.107 or t = 63.435 o
BUT since the rectangular coordinates x and y are both negative, the point is in quadrant III and we need to add Pi or 180 o to the value of t given by the calculator. Hence the polar angle t is given by
t = 4.249 or t = 243.435 o
Point (-2 , -4) in rectangular coordinates may be written in polar for as follows.
( 5 sqrt ( 2 ) , 4.249 ) or ( 5 sqrt ( 2 ) , 243.435 o )
More references on polar coordinates and trigonometry topics.