函数f(x)=Asin(wx+y)(A不等于0,w不等于0),g(x)=Acos(wx+y),若对于任意实数x恒有f(π/3+x)=f(π/3-x)试求g(π/3)的值

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函数f(x)=Asin(wx+y)(A不等于0,w不等于0),g(x)=Acos(wx+y),若对于任意实数x恒有f(π/3+x)=f(π/3-x)试求g(π/3)的值函数f(x)=Asin(wx+y

函数f(x)=Asin(wx+y)(A不等于0,w不等于0),g(x)=Acos(wx+y),若对于任意实数x恒有f(π/3+x)=f(π/3-x)试求g(π/3)的值
函数f(x)=Asin(wx+y)(A不等于0,w不等于0),g(x)=Acos(wx+y),若对于任意实数x恒有f(π/3+x)=f(π/3-x)
试求g(π/3)的值

函数f(x)=Asin(wx+y)(A不等于0,w不等于0),g(x)=Acos(wx+y),若对于任意实数x恒有f(π/3+x)=f(π/3-x)试求g(π/3)的值
∵f(π/3+x)=f(π/3-x)
∴Asin(πω/3+xω+y)=Asin(πω/3-xω+y)
∴πω/3+y=nπ/2(n=1、3、5、7、9、……)
g(π/3)=Acos(πω/3+y)=Acos(nπ/2)
∵cos(π/2)=0;cos(3π/2)=0;cos(5π/2)=0;cos(7π/2)=0……
∴g(π/3)=0