But with the http://www.mathopenref.com/dmscalculator.html calculator, if I enter 0° 0' 59" and then add -0° 1' 0", I get -0° 0' 1". Surely the only way that can happen is if -0° 1' 0" represents a negative angle of 0° 1' 0", i.e., an angle of -1'. (Understandably, the calculator won't let you enter angles like 0° -1' 0" or 0° 0' 60".)