求函数y=cos+(√3)sinx,x∈[π/6,2π/3]的值域
问题描述：
求函数y=cos+(√3)sinx,x∈[π/6,2π/3]的值域
答
y=cos+(√3)sinx
=2（1/2cosx+√3/2sinx）
=2(sinπ/6cosx+cosπ/6sinx)
=2 sin(π/6+x)
x∈[π/6,2π/3] π/6+x∈[π/3,5π/6] sin(π/6+x)∈[1/2,1]
y∈[1,2]
答
y=2(sinx*√3/2+cosx*1/2)
=2(sinxcosπ/6+cosxsinπ/6)
=2sin(x+π/6)
π/3