已知函数f x 根号3sin(wx+φ)-cos(wx+φ)(w>0,0

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已知函数f x 根号3sin(wx+φ)-cos(wx+φ)(w>0,0
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已知函数f x 根号3sin(wx+φ)-cos(wx+φ)(w>0,0
已知函数f x 根号3sin(wx+φ)-cos(wx+φ)(w>0,0

已知函数f x 根号3sin(wx+φ)-cos(wx+φ)(w>0,0
f(x)=(√3)sin(ωx+φ)-cos(ωx+φ)
=2{[(√3)/2]sin(ωx+φ)-(1/2)cos(ωx+φ)}
=2[sin(π/3)sin(ωx+φ)-cos(π/3)cos(ωx+φ)]
=-2cos(ωx+φ+π/3)
f(-x)=-2cos(-ωx+φ+π/3)
因为f(-x)=f(x)
所以cos(φ+π/3-ωx)=cos(φ+π/3+ωx)
所以φ+π/3=kπ,k∈Z
因为0

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