MapBasic Code. Copy/Paste if needed.
include "GC_Coordinates.def"

'======================================================================
sub GreatCircleCoords (
   byval fLon0 as float,      'Origin longitude
   byval fLat0 as float,      'Origin latitude
   byval fAzimuth as float,   'Azimuth
   byval fDistance as float,  'Distance
   byval fRadius as float,    'Radius of sphere
   fLon1 as float,            'Destination longitude
   fLat1 as float)            'Destination latitude

'Calculates lat/lon coords from origin, azimuth and distance from
'origin. Returned coordinates are in decimal degrees. fDistance and
'fRadius must be in the same units.
'----------------------------------------------------------------------
dim c as float
dim lat0, lon0 as float
dim Az as float
dim a, b as float

   'convert to radians
   Az = fAzimuth * DEG2RAD
   lat0 = fLat0 * DEG2RAD
   lon0 = fLon0 * DEG2RAD

   'calculate great circle arc for this distance
   c = ((fDistance / (2 * PI * fRadius)) * 360.0) * DEG2RAD

   fLat1 = asin( sin(lat0) * cos(c)
      + cos(lat0) * sin(c) * cos(Az)) * RAD2DEG
   a = sin(c) * sin(Az)
   b = cos(lat0) * cos(c) - sin(lat0) * sin(c) * cos(Az)
   if b = 0 then
      fLon1 = fLon0
      exit sub
   end if

   fLon1 = fLon0 + atn(a/b) * RAD2DEG
end sub