已知函数f x=√3sin(wx+φ/2)*cos(wx+φ/2)+sin^2(wx+φ/2)(w>0,0

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已知函数f x=√3sin(wx+φ/2)*cos(wx+φ/2)+sin^2(wx+φ/2)(w>0,0
已知函数f x=√3sin(wx+φ/2)*cos(wx+φ/2)+sin^2(wx+φ/2)(w>0,0

已知函数f x=√3sin(wx+φ/2)*cos(wx+φ/2)+sin^2(wx+φ/2)(w>0,0
f (x)=√3sin(wx+φ/2)*cos(wx+φ/2)+sin^2(wx+φ/2)
=(√3/2)sin(2wx+φ)+(1/2)[1-cos(2wx+φ)]
=sin(2wx+φ-π/6)+1/2,
y=f(x)的图像过点(π/3,1)
∴sin(2wπ/3+φ-π/6）=1/2,
其图像最高点与相邻对称中心的距离为√（1+T^2/16)=√(9/4+π^2/16),
其中T是f(x)的最小正周期.
题目似乎有误

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