I'm doing work on polar coordinates in double integrals. Could someone explain why when circles aren't centered on the origin the angle only varies from (if it is translated above the origin) 0 to pi. I thought the angle was supposed to be the angle in the circle, so if its a full circle then 0 to 2pi. This is the same for when its translated right, the angle only varies from -pi/2 to pi/2.... I would have thought as its a full circle it is again 0 to 2pi. Where does this angle come from?