Mathematics

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Find the maximum or minimum values of sin x+sin y+sin(x+y)

  • Mathematics -

    z = sinx + siny + sin(x+y)
    to find the maxima, we need

    ∂z/∂x = 0 and ∂z/∂y = 0

    ∂z/∂x = cosx + cos(x+y)
    ∂z/∂y = cosy + cos(x+y)

    ∂z/dx = 0 when x+y = pi-x
    A handy place for this is at (pi/3,pi/3)

    z(pi/3,pi/3) = √3/2 + √3/2 + √3/2 = 3√3/2 = 2.598

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