Question

f(x)=sinx-根号3cosx,（-π≤x≤0）的值域为

Answer 1

f(x)＝sinx－√3cosx＝2(1/2sinx－√3/2cosx)＝2sin(x－π/3)

∵﹣π≤x≤0 ∴﹣4π/3≤x－π/3≤﹣π/3

∴﹣1≤sin(x－π/3)≤√3/2

∴f(x)＝sinx－√3cosx(﹣π≤x≤0)的值域为[﹣1,√3/2]