Question

函数f(x)=sinx-根号3cosx(x∈【-π,0】)的值域为

Answer 1

f(x)=sinx-根号3cosx
=2[sinx*(1/2)-cosx*(√3/2)]
=2[sinx*cos(π/3)-cosx*sin(π/3)]
=2sin(x-π/3)
x∈【-π,0】
x-π/3∈【-4π/3,-π/3】
sin(x-π/3)∈【-1,√3/2】
所以 y∈【-2,√3】

Answer 2

f(x)=sinx-根号3cosx
=2(1/2*sinx-√3/2*cosx)
=2(sinxcosπ/3-cosxsinπ/3)
=2sin(x-π/3)
∵x∈【-π,0】x-π/3∈【-4π/3,-π/3】
∴-1≤sin(x-π/3)≤√3/2 -2≤ f(x)≤√3
f(x)值域为[-2,√3]

Answer 3

f(x)=sinx-√3cosx=f(x)=sinx-f(x)=2*（1/2sinx-√3/2cosx）=2*（sinxcos(π/3)-sin(π/3)cosx)
=2*sin(x-π/3)
x-π/3的范围是-4π/3到-π/3

所以最小值-2，最大值√3

Answer 4

f(x)=2sin(x-π/3) -4π/3＜x-π/3＜-π/3 -2＜f(x)＜√3