Your area formula is the best one to use.
Don't forget to convert all angles to radians.
Given the problem:
Two sides of a triangle measure 9 in. and 6 in. The measure of the inclusive angle changes from to . Use differentials to approximate the change in the area of the triangle.
I used , where a and b are the lengths of the sides and C is the included angle, for my area function. I am just wondering if anyone has another approach for the area equation that would work well with this problem.