已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π)已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π/3+x)=f(π/3-x),试求个(π/3)的值试求g(π/3)的
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![已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π)已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π/3+x)=f(π/3-x),试求个(π/3)的值试求g(π/3)的](/uploads/image/z/8621697-57-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3DAsin%28%CF%89x%2B%CF%86%29%28A%E2%89%A00%2C%CF%89%E2%89%A00%29%2Cg%28x%29%3DAcos%28%CF%89x%2B%CF%86%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%28%CF%80%29%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3DAsin%28%CF%89x%2B%CF%86%29%28A%E2%89%A00%2C%CF%89%E2%89%A00%29%2Cg%28x%29%3DAcos%28%CF%89x%2B%CF%86%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%28%CF%80%2F3%2Bx%29%3Df%28%CF%80%2F3-x%29%2C%E8%AF%95%E6%B1%82%E4%B8%AA%EF%BC%88%CF%80%2F3%EF%BC%89%E7%9A%84%E5%80%BC%E8%AF%95%E6%B1%82g%EF%BC%88%CF%80%2F3%EF%BC%89%E7%9A%84)
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已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π)已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π/3+x)=f(π/3-x),试求个(π/3)的值试求g(π/3)的
已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π)
已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π/3+x
)=f(π/3-x),试求个(π/3)的值
试求g(π/3)的值
已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π)已知函数f(x)=Asin(ωx+φ)(A≠0,ω≠0),g(x)=Acos(ωx+φ),若对于任意实数x恒有f(π/3+x)=f(π/3-x),试求个(π/3)的值试求g(π/3)的
f(π/3+x)=Asin(π/3*ω+ωx+φ)=Asin(π/3*ω+φ)cos(ωx)+Acos(π/3*ω+φ)sin(ωx)
f(π/3-x)=Asin(π/3*ω-ωx+φ)=Asin(π/3*ω+φ)cos(ωx)-Acos(π/3*ω+φ)sin(ωx)
令上两式相等则有
Acos(π/3*ω+φ)sin(ωx)=-Acos(π/3*ω+φ)sin(ωx)
可得cos(π/3*ω+φ)=0
得g(π/3)=Acos(π/3*ω+φ)sin(ωx)=0
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