Y=负2sinX[sin(x-派/6)],求他的化简,级最小正周期和最大值,

Question

Y=负2sinX[sin(x-派/6)],求他的化简,级最小正周期和最大值,

Answer 1

y = -2sinx[sin(x-π/6)]
= -2sinx(sinxcosπ/6-cosxsinπ/6)
= -2sinx(√3/2 sinx - 1/2 cosx)
= - √3sin^2x - sinxcosx
= -√3(1-cos2x)/2 - 1/2 sin2x
= -√3/2 + √3/2 cos2x - 1/2 sin2x
= - (1/2 sin2x - √3/2 cos2x) - √3/2
= - sin(2x-π/3) - √3/2
最小正周期：2π/2 = π
sin(2x-π/3) ≤1, sin(2x-π/3)- √3/2 ≤（2-√3)/2,最大值（2-√3)/2