余弦公式的串行定律

# \'lat\' short for \'latitude\', \'lng\' short for \'longitude\'.
# EARTH_RADIUS = 6371000.0, unit is meter.
#
distance = Math.acos( Math.sin(lat1)*Math.sin(lat2) + 
           Math.cos(lat1)*Math.cos(lat2) * 
           Math.cos(lng2-lng1)) * EARTH_RADIUS

# lat1 == lat2 == lat
# \'distance\' and \'lng\' are known 
lng2 = Math.acos((Math.cos(distance/EARTH_RADIUS) - Math.sin(lat)*Math.sin(lat))/(Math.cos(lat)*Math.cos(lat))) + lng

lat_degrees =  -89.8345981836319  
lng_degrees = 96.42309331893921
lat = lat1 = lat2 = (lat_degrees * Math::PI)/180 # -1.567909520510494
lng = (lng_degrees * Math::PI)/180  # 1.682900453373236 
distance = 67544.06725769254

Math::DomainError: Numerical argument is out of domain - \"acos\"