Converting Universal Transverse Mercator to Lat/Long and back

Spherical trigonometry to transform and rotate points through space
Good luck doing this one on a pocket calculator!
Enter PROJ.4, a cartographic projections library

cs2cs +proj=latlong +datum=NAD83 +to +proj=utm +zone=10 +datum=NAD27

cs2cs can also do DMS to decimal and back:

cs2cs -f "%.6f" +proj=latlong +to +proj=latlong

PROJ.4 lives at http://remotesensing.org/proj/

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