已知函数f(x)=2sin(ωx-π/6) (ω>0)和g(x)=cos(2x+φ)-3的图象的对称轴完全相同.若X属于【-π/3,π/6】,则f(x)的取值范围是?
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![已知函数f(x)=2sin(ωx-π/6) (ω>0)和g(x)=cos(2x+φ)-3的图象的对称轴完全相同.若X属于【-π/3,π/6】,则f(x)的取值范围是?](/uploads/image/z/1858874-50-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%28%CF%89x-%CF%80%2F6%29+%28%CF%89%3E0%29%E5%92%8Cg%28x%29%3Dcos%282x%2B%CF%86%29-3%E7%9A%84%E5%9B%BE%E8%B1%A1%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E5%AE%8C%E5%85%A8%E7%9B%B8%E5%90%8C.%E8%8B%A5X%E5%B1%9E%E4%BA%8E%E3%80%90-%CF%80%2F3%2C%CF%80%2F6%E3%80%91%2C%E5%88%99f%28x%29%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%3F)
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已知函数f(x)=2sin(ωx-π/6) (ω>0)和g(x)=cos(2x+φ)-3的图象的对称轴完全相同.若X属于【-π/3,π/6】,则f(x)的取值范围是?
已知函数f(x)=2sin(ωx-π/6) (ω>0)和g(x)=cos(2x+φ)-3的图象的对称轴完全相同.若X属于【-π/3,π/6】,
则f(x)的取值范围是?
已知函数f(x)=2sin(ωx-π/6) (ω>0)和g(x)=cos(2x+φ)-3的图象的对称轴完全相同.若X属于【-π/3,π/6】,则f(x)的取值范围是?
已知函数f(x)=2sin(ωx-π/6) (ω>0)和g(x)=cos(2x+φ)-3的图象的对称轴完全相同.若X属于【-π/3,π/6】,则f(x)的取值范围是?
令ωx-π/6=π/2+kπ,得f(x)的对称轴为:x=2π/3ω+kπ/ω;
再令2x+φ=kπ,即得g(x)的对称轴为:x=-φ/2+kπ/2;
二者的对称轴完全相同,即有2π/3ω+kπ/ω=-φ/2+kπ/2;
于是得2π/3ω=-φ/2.(1);kπ/ω=kπ/2.(2)
由(2)得ω=2;代入(1)式得φ=-2π/3.
故f(x)=2sin(2x-π/6),当-π/3≦x≦π/6时,minf(x)=f(-π/4)=2sin(-π/2-π/6)=-2cos(π/6)=-√3
maxf(x)=f(π/6)=2sin(π/3-π/6)=2sin(π/6)=1.
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