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](/uploads/image/z/10193151-39-1.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3DAsin%28wx%2By%29%28A%E4%B8%8D%E7%AD%89%E4%BA%8E0%2Cw%E4%B8%8D%E7%AD%89%E4%BA%8E0%29%2Cg%28x%29%3DAcos%28wx%2By%29%2C%E8%8B%A5%E5%AF%B9%E4%BA%8E%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0x%E6%81%92%E6%9C%89f%EF%BC%88%CF%80%2F3%2Bx%EF%BC%89%3Df%EF%BC%88%CF%80%2F3-x%EF%BC%89%E8%AF%95%E6%B1%82g%EF%BC%88%CF%80%2F3%EF%BC%89%E7%9A%84%E5%80%BC)
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
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