函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示. ①求f(函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示.①求f(x)的最小正周期及解析式.②设函数g(x)=f(x)-cos2x,求g(x)在
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![函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示. ①求f(函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示.①求f(x)的最小正周期及解析式.②设函数g(x)=f(x)-cos2x,求g(x)在](/uploads/image/z/6607280-56-0.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3DAsin%28%CF%89x%2B%CF%86%29%EF%BC%88A%EF%BC%9E0%2C%CF%89%EF%BC%9E0%2C%7C%CF%86%7C%EF%BC%9C%CF%80%2F2%EF%BC%89%E7%9A%84%E9%83%A8%E5%88%86%E5%9B%BE%E5%83%8F%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA.+%E2%91%A0%E6%B1%82f%28%E5%87%BD%E6%95%B0f%28x%29%3DAsin%28%CF%89x%2B%CF%86%29%EF%BC%88A%EF%BC%9E0%2C%CF%89%EF%BC%9E0%2C%7C%CF%86%7C%EF%BC%9C%CF%80%2F2%EF%BC%89%E7%9A%84%E9%83%A8%E5%88%86%E5%9B%BE%E5%83%8F%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA.%E2%91%A0%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%8F%8A%E8%A7%A3%E6%9E%90%E5%BC%8F.%E2%91%A1%E8%AE%BE%E5%87%BD%E6%95%B0g%28x%29%3Df%28x%29-cos2x%2C%E6%B1%82g%28x%29%E5%9C%A8)
函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示. ①求f(函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示.①求f(x)的最小正周期及解析式.②设函数g(x)=f(x)-cos2x,求g(x)在
函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示. ①求f(
函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示.
①求f(x)的最小正周期及解析式.
②设函数g(x)=f(x)-cos2x,求g(x)在区间[0,π/2]上的最小值.
函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示. ①求f(函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)的部分图像如图所示.①求f(x)的最小正周期及解析式.②设函数g(x)=f(x)-cos2x,求g(x)在
①
函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|<π/2)
根据图像知A=1,
半周期T/2=2π/3-π/6=π/2,T=π
根据2π/w=π得:w=2
又x=π/6,f(x)取得最大值1
则sin(2*π/6+φ)=1,φ+π/3=π/2+2kπ,k∈Z
∴φ=π/6+2kπ,k∈Z
∵|φ|<π/2 ∴φ=π/6
∴f(x)的最小正周期T=π
解析式f(x)=sin(2x+π/6)
②
g(x)=f(x)-cos2x
=sin(2x+π/6)-cos2x
=sin2xcosπ/6+cos2xsinπ/6-cos2x
=sin2xcosπ/6-cos2xsinπ/6
=sin(2x-π/6)
∵0≤x≤π/2
∴-π/6≤2x-π/6≤5π/6
∴当2x-π/6=-π/6时,g(x)取得最小值-1/2