Monday, November 29, 2010

Fox 319


  1. I'd think that the maximum value occurs when α=β=θ or Max[(sin(α)*sin(β)*sin(θ)] =3√3/8

  2. Henkie, see six' solution below:

    six said...
    So we have,

    x + y + z = 360 and sinx*siny*sinz

    -> f(x,y) = sin(x)*sin(y)*sin(360-x-y)
    -> f(x,y) = sin(x)*sin(y)*-sin(x+y)

    Now to find the critical points of f(x,y), we just need to find the partial derivative with respect to x and y and solve for 0.

    f_x(x,y) =


    solve for 0.


    -> tan(x) = -tan(x+y)

    Since the function is symmetric, we should get the same partial derivative for y.

    -> tan(y) = -tan(y+x)

    -> tan(x)=tan(y)

    -> x = y or they are opposites. However, if they are opposites, the original function just becomes 0. Thus, x = y.

    Now substitute in x for y in the original equation and find its critical points.

    Eventually, you will get sin(3x)=0

    x = 120 degrees
    y = 120 degrees
    z = 120 degrees

    Answer (D)