UTM Zone overlap

[mackrackit]

Not really PIC related, but a part of the project has a PIC in it.

I thought I understood the UTM system. Northing is referenced from the equator and Easting works from the zone's meridian with a value of 500,000.

A couple of weeks ago I received a set of coordinates that claimed to be in the zone of 12S. The Easting is 0147491. Clearly in zone 11S. When I entered the coordinates into my GPS to try and find the zone 11S equivalent, the GPS did make the change, but to my surprise the Northing changed also.

So my question is... If the Northing is referenced from the equator. Why does/did the Northing change when the coordinate is projected in the wrong zone? I figure the Easting is the only part that should change.

I would guess some one pulled these coordinates from a map projected in 12S. Now to get them back to 11S.

[mackrackit]

Still working on this.

Found some formulas that are helping in my confusion.

I thought converting from Radian to Degrees was simple enough, divide by PI mult by 180 and so forth. But that is not working.

So I went back to the old trig book and refreshed myself on (at least I tried to) radians and things.

My calculator shows:
COSINE of 2 in DEGREES = 0.99939082

COSINE of 2 in RADIANS = -0.41614683

Now if I want to convert Radians to degrees I do this:
COSINE of (2 / 57.29577951) in RADIANS = 0.99939082

My question is... How do I go the other way?
COSINE of 2 ??? in DEGREES = -0.41614683