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Trigonometric simplification for distance on a sphere

asked 2013-07-20 23:53:30 -0600

updated 2015-01-14 07:24:17 -0600

FrédéricC gravatar image

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... ) 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!

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answered 2013-07-21 02:49:50 -0600

Volker Braun gravatar image

Doesn't look like they are equal, typo?

sage: diff(0.1, 0.2, 0.3)
-0.264329471853371
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Asked: 2013-07-20 23:53:30 -0600

Seen: 103 times

Last updated: Jul 21 '13