Question

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

Answer 1

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