rectToPolarGood

 convert the rectangular coords (x, y) to polar coordinates 
USAGE: [r,theta]=rectToPolarGood(1, sqrt(3))
r =
    2.0000
theta =
   1.0472
>> theta*180/pi
ans =
   60.0000
=================================================================   
     r     =  magnitude of the vector
     theta =  angle of the theta with respect to the x-axis,
              positive in the counter-clockwise direction,
              in units of radians.  The value of theta ranges from 0 to 2pi

function[r, theta] = rectToPolarGood(x, y)
% convert the rectangular coords (x, y) to polar coordinates
%USAGE: [r,theta]=rectToPolarGood(1, sqrt(3))
%r =
%    2.0000
%theta =
%   1.0472
%>> theta*180/pi
%ans =
%   60.0000
%=================================================================
%     r     =  magnitude of the vector
%     theta =  angle of the theta with respect to the x-axis,
%              positive in the counter-clockwise direction,
%              in units of radians.  The value of theta ranges from 0 to 2pi

  % first, calculate the magnitude of the vector
  r = sqrt(x*x + y*y);

  % next, the angle.  We have to deal with the case of x = 0 carefully;
  %   if both x and y are zero, return an angle of 0.
  if (x == 0) 
    if (y > 0)
      theta = pi/2;
    elseif (y < 0)
      theta = 3*pi/2;
    else
      theta = 0;
    end
  else
    theta = atan(y/x);
  end

  % now we have to find the proper quadrant, and adjust the angle
  %   theta if necessary
  if ((x > 0) & (y > 0))
  % quadrant 1: no adjustment needed
  elseif ((x > 0) & (y < 0)) 
  % quadrant 4: we must add 2pi to the angle returned by the 'atan' function
    theta = theta + 2*pi;
  elseif ((x < 0) & (y > 0))
  % quadrant 2: must add pi to the angle returned by 'atan' function
    theta = theta + pi;
  elseif ((x < 0) & (y < 0))
  % quadrant 3: must add pi to angle returned by 'atan' function
    theta = theta + pi;
end