This is my database table (spots).

Given a point on map P(longitude, latitude), what I want to retrieve from the database is the set of points within a given radius where P is the center. I tried a simple query using the simple formula of Longitude and Latitude, unfortunately the result is always null 🙁 . What am I doing wrong here? Any idea?
$sql = "SELECT * FROM $tbl_name
WHERE ACOS(SIN('".$latitude."') * SIN(spots.latitude) + COS('".$latitude."') * COS(spots.latitude) * COS(spots.longitude - '".$longitude ."')) * 6371 <= '".$radius."'";
Based on Cameron S’s & MrGlass’s ideas, and a bit searching over the Internet, I found one working solution: