求周期及最大值最小值y=sin(x-π/3)cos x

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求周期及最大值最小值y=sin(x-π/3)cos x

求周期及最大值最小值y=sin(x-π/3)cos x
求周期及最大值最小值
y=sin(x-π/3)cos x

求周期及最大值最小值y=sin(x-π/3)cos x
y=sin(x-π/3)cosx
=[sinxcos(π/3)-cosxsin(π/3)]cosx
=[(1/2)*sinx-(√3/2)*cosx]cosx
=(1/2)*sinxcosx-(√3/2)*(cosx)^2
=(1/4)sin2x-(√3/2)*(1+cos2x)/2
=(1/4)sin2x-(√3/4)cos2x-√3/4
=√(1/16+3/16)sin(2x-π/3)-√3/4
=(1/2)sin(2x-π/3)-√3/4
所以T=2π/2=π
最大值是1/2-√3/4=(2-√3)/4,最小值是-1/2-√3/4=(-2-√3)/4