For the maximum value of a trigonometric function with special coefficients in △ ABC , three solutions of analysis segment, the Lagrange multiplier, the inequalities, are first proposed, leading to the same result. Then for a general trigonometric function with the coefficients ,b, and c belonging to ，the Lagrange multiplier is used to seek its maximum value. Finally, the solution to the extreme value of the trigonometric function with the coefficients , b, and c belonging to is derived