$A = -4;
$w = 500;
then

$re =
'/^\s*(\Q$A\E\s*\*?\s*\Qcos\E\s+\Q$w\E\s*\Qt\E\s+\QA\E||\Q$A\E\s*\*?\s*\Qcos\E\s*\(\s*\Q$w\E\s*\Qt\E\s*\)\s+\QA\E)\s*$/';

will accept answers in the following form:
-4cos 500t A
-4 cos 500t A
-4*cos 500t A
-4*cos(500t) A   -- and any number of spaces before and after *, t, ( and )