f(x)=sinx-根号3cosx,(-π≤x≤0)的值域为

1个回答

  • f(x)=sinx-√3cosx

    =2(1/2sinx-√3/2cosx)

    =2[sinxcos(π/3)-cosxsin(π/3)]

    =2sin(x-π/3)

    因为-π≤x≤0,则-4π/3≤x-π/3≤-π/3

    由y=sinx的函数图像可得

    当x-π/3=-π/2时,sin(x-π/3)取得最小值-1,此时f(x)取得最小值1×(-2)=-2(-2取得到)

    当x-π/3=-4π/3时,sin(x-π/3)取得最大值1/2,此时f(x)取得最大值1×1/2=1(1取不到)

    所以f(x)=sinx-根号3cosx,(-π≤x≤0)的值域为[-2,1)