from mysql 5.1, 5.5, 5.6, 5.7 manual

http://dev.mysql.com/doc/refman/5.1/en/mathematical-functions.html#function_cot

http://dev.mysql.com/doc/refman/5.5/en/mathematical-functions.html#function_cot

http://dev.mysql.com/doc/refman/5.6/en/mathematical-functions.html#function_cot

http://dev.mysql.com/doc/refman/5.7/en/mathematical-functions.html#function_cot

•  COT(X)

  Returns the cotangent of X.

  mysql> SELECT COT(12);
          -> -1.5726734063977
  mysql> SELECT COT(0);
          -> NULL

maybe a sql_mode parameter change the output of this function?