Maximum value of

Question

12sinΘ-9sin²Θ

Answer 1

This problem can be solved very easily with calculus.     At the maximum value of θ ,  the derivative of the

expression will be zero.   

This derivative is    12 cos(θ) - 18 sin(θ) cos(θ)   setting this to zero results in

12 - 18 sin(θ) =0     (after dividing through by cos(θ)   )  So

  sin(θ) = 2/3    substituting back into the expression yields the value 4.

 

This can be checked using a graphing calculator.