y=sinθ+√3cosθを合成すると
y=2sin(θ+π/3)
sinθの値域は-1≦sinθ≦1より-2≦2sinθ≦2
∴sinθの最大値はπ/2の時、最小値は3π/2の時であるからθ+π/3=π/2 θ=π/6の時最大値2
θ+π/3=3π/2 θ=7π/6の時最小値-2
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