I want to calculate a pair of GPS coordinates(lat,long) that is at x meters N/S/E/W from a known point (lat\_old,long\_old). 


I have found the Haversine formula
<http://upload.wikimedia.org/math/0/5/5/055b634f6fe6c8d370c9fa48613dd7f9.png>
for a for the distance between a two points and I have tried to isolate lat , but the formula I get (through wolfram alpha) is divided by havesine(long-long\_old) , so i get a divide by 0, what am I doing wrong? Should I use other formula?



Calculate GPS coordinates at x meters
I have to do a little guessing in answering your question: 


I suppose, you are given WGS84 coordinates and an ellipsoid that approximates the shape of the earth, and you have the task of finding the WGS84 coordinates, that has an offset of x meters to the east and y meters to the north. 


In that case you don't need the Haversine formula; you rather need to know, that the cross sections of the ellipsoid are circles in case of planes, that are parallel to the equator and, ellipses in case of planes, that contain the north and south pole. 


The hard part of your task is to calculate, what fraction of the cross-sectional ellipse's circumference the given y-meters correspond to (depends on latitude and, whether it is in north or south direction) and then multiply that fraction by 360°, which gives you the WG84-delta in south/north direction.  

Once you have calculated that, you can calculate the radius of the circle, that is parallel to the equator and from the radius of that circle you can calculate, how many degrees your given x meters correspond to. 


The Haversine formula is only needed to calculate the geodesic distance between two WGS84 coordinates, if you are given the parameters of the rotational ellipsoid, that approximates the earth's surface.


