已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|

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已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|

已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|
已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|

已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|
已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|0,w>0,|φ|T=4π==>w=2π/T=1/2
∴f(x)=2sin(1/2x+φ)
∵f(x)图像关于直线x=π/3对称,
∴f(x)在Y轴右侧第一个对称轴为:wx+φ=π/2==>x=(π-2φ)/(2w)
令(π-2φ)/(2w)=π/3==>(π-2φ)=π/3==>φ=π/3
∴f(x)=2sin(1/2x+π/3)
(2)解析:∵在锐角△ABC中,f(2A)=2sin(A+π/3)=√3,
∴A+π/3=2π/3==>A=π/3==>B+C=2π/3==>C=2π/3-B
sinB+sinC=sinB+sin(2π/3-B)=√3sin(B+π/6)
∵0