函數(shù)f(x)=sinx/2+αcosx/2的圖像關(guān)于直線x=π/3對稱
∴ x=0和x=2π/3所對應(yīng)的函數(shù)值相等
即 f(0)=f(2π/3)
∴ sin0+αcos0=sin(π/3)+αcos(π/3)
∴ 0+α=√3/2+α*(1/2)
∴ (1/2)α=√3/2
∴α=√3
即常數(shù)α的值等于√3