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Richard P. | Fairfax County Tutor for HS Math and ScienceFairfax County Tutor for HS Math and Sci...
4.9 4.9 (628 lesson ratings) (628)
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.