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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)=2asin(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!

 2 No.2 Revision calc314 4151 ●21 ●48 ●111

Trigonometric simplification for distance on a sphere

These are two equivalent equations for distance on a sphere:

hav(x)=sin(x/2)^2

hav(x)=sin(x/2)^2
dist1(lat1, lat2, dLon)=2asin(hav(lat1-lat2)+cos(lat1)cos(lat2)*hav(dLon))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))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(x,y,z)=dist1(x,y,z)-dist2(x,y,z)
diff.simplify_full()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!

 3 retagged FrédéricC 4284 ●3 ●37 ●89

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!