If you are not worried about the curvature of the earth's surface then this turns into something really easy.
You change all of the latitude and longitudes into a polar coordinate based system (angle and magnitude from your own latitude and longitude). Then you get the device's compass bearing. Then you adjust all of the "friend's" angles based off your device's angle. Then plot everything out on your map (translating your polar coordinates back to cartesian). Then update whenever the device's compass bearing changes (or friend's location updates).
It's a lot of math, but the process is pretty straight forward and you should be able to get all of the conversion information with a single google search.