已知函数f(x)=√3sin(wx+φ)-cos(wx+φ)(0

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已知函数f(x)=√3sin(wx+φ)-cos(wx+φ)(0
已知函数f(x)=√3sin(wx+φ)-cos(wx+φ)(0

已知函数f(x)=√3sin(wx+φ)-cos(wx+φ)(0
f(x)=√3sin(wx+φ)-cos(wx+φ)
=2[√3/2sin(wx+φ)-1/2cos(wx+φ)]
=2sin(wx+φ-π/6)
对称轴：令wx+φ-π/6=kπ+π/2（k∈Z)
解之：x=（kπ+2π/3-φ）/w
故两相邻对称轴间的距离为π/|w|=π/2
又w>0
故w=2
又y=f(x)为偶函数
故x=0是他的一条对称轴
故φ-π/6=kπ+π/2
即φ=kπ+2π/3（k∈Z)
又0

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