ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 21 Jul 2013 06:53:30 +0200Trigonometric simplification for distance on a spherehttps://ask.sagemath.org/question/10369/trigonometric-simplification-for-distance-on-a-sphere/These are two equivalent equations for distance on a sphere:
hav(x)=sin(x/2)^2
dist1(lat1, lat2, dLon)=2*asin(hav(lat1-lat2)+cos(lat1)*cos(lat2)*hav(dLon))
dist2(lat1, lat2, dLon)=acos(sin(lat1)*sin(lat2)+cos(lat1)*cos(lat2)*cos(dLon))
(According to http://www.movable-type.co.uk/scripts/latlong.html )
Indeed numerically they evaluate equal.
But why their difference does not simplify to 0?
diff(x,y,z)=dist1(x,y,z)-dist2(x,y,z)
diff.simplify_full()
Am I doing something wrong? Is there a way to have Sage prove the two forms are equivalent, or to transform one to another?
Thanks!
Mihai PredaSun, 21 Jul 2013 06:53:30 +0200https://ask.sagemath.org/question/10369/