Question

求解需要详细步骤的最好写在草稿纸上

Answer 1

追问

感谢

Answer 2

14.

f(x)=sinx-√3cosx

=2[(1/2)sinx-(√3/2)cosx]

=2[sinxcos(π/3)-cosxsin(π/3)]

=2sin(x-π/3)

最小正周期T=2π/1=2π

sin(x-π/3)=1时，f(x)取得最大值f(x)max=2

sin(x-π/3)=-1时，f(x)取得最小值f(x)min=-2

15.

f(x)=cos(2x)+2√3sinxcosx

=cos(2x)+√3sin(2x)

=2[(√3/2)sin(2x)+(1/2)cos(2x)]

=2[sin(2x)cos(π/6)+cos(2x)sin(π/6)]

=2sin(2x+π/6)

最小正周期T=2π/2=π

sin(2x+π/6)=1时，f(x)取得最大值f(x)max=2

sin(2x+π/6)=-1时，f(x)取得最小值f(x)min=-2

Answer 3

14、f(x)=2[(1/2)sinx - (√3/2)cosx]
=2sin(x - π/3)
∴T=2π/1=2π
∵正弦函数的值域是[-1，1]
∴最大值是2，最小值是-2