Convert the rectangular coordinates (4√3,−4) to polar form. Let r>0 and 0≤θ<2π.

You have a point (x, y) and, I'm assuming, you want to convert it into  r·cis( theta)  form.

 

If you do:  r  =  sqrt( x² + y² )       

and    theta  =  tan^-1( y/x ).           

 

Since the point ( 4sqrt(3), -4 )  is in the fourth quadrant, make certain that your angle is also in the fourth quadrant.