The ` atan2` function is used mostly to convert from rectangular (x,y) to polar (r,theta) (r,th) coordinates that must satisfy x = r*cos theta r*costh and y = r*sin theta. r*sinth. These equations are satisfied when (x=0,y=0) is mapped to (r=0,theta=0). (r=0,th=0). In general, conversions to polar coordinates should be computed thus:

r := hypot(x,y); ... := sqrt(x*x+y*y)

theta := atan2(y,x).

r := hypot(x,y); ... := v/(x^{}^{2}^{0}+y^{}^{2}^{0})

th := atan2(y,x).