已知函数f(x)=sin(ωx+φ)(ω>0,0≤φ≤∏)为偶函数,其图像上的两个个最高点之间的距离为2π(1)求f(X)的解析式(2)若α∈(-π/3,π/2),f(α+π/3)=1/3,求sin(2α+5π/3)的值
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![已知函数f(x)=sin(ωx+φ)(ω>0,0≤φ≤∏)为偶函数,其图像上的两个个最高点之间的距离为2π(1)求f(X)的解析式(2)若α∈(-π/3,π/2),f(α+π/3)=1/3,求sin(2α+5π/3)的值](/uploads/image/z/2834336-56-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28%CF%89x%2B%CF%86%29%28%CF%89%3E0%2C0%E2%89%A4%CF%86%E2%89%A4%E2%88%8F%29%E4%B8%BA%E5%81%B6%E5%87%BD%E6%95%B0%2C%E5%85%B6%E5%9B%BE%E5%83%8F%E4%B8%8A%E7%9A%84%E4%B8%A4%E4%B8%AA%E4%B8%AA%E6%9C%80%E9%AB%98%E7%82%B9%E4%B9%8B%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA2%CF%80%EF%BC%881%EF%BC%89%E6%B1%82f%28X%29%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%EF%BC%882%EF%BC%89%E8%8B%A5%CE%B1%E2%88%88%EF%BC%88-%CF%80%2F3%2C%CF%80%2F2%EF%BC%89%2Cf%EF%BC%88%CE%B1%2B%CF%80%2F3%EF%BC%89%3D1%2F3%2C%E6%B1%82sin%EF%BC%882%CE%B1%2B5%CF%80%2F3%EF%BC%89%E7%9A%84%E5%80%BC)
已知函数f(x)=sin(ωx+φ)(ω>0,0≤φ≤∏)为偶函数,其图像上的两个个最高点之间的距离为2π(1)求f(X)的解析式(2)若α∈(-π/3,π/2),f(α+π/3)=1/3,求sin(2α+5π/3)的值
已知函数f(x)=sin(ωx+φ)(ω>0,0≤φ≤∏)为偶函数,其图像上的两个个最高点之间的距离为2π
(1)求f(X)的解析式
(2)若α∈(-π/3,π/2),f(α+π/3)=1/3,求sin(2α+5π/3)的值
已知函数f(x)=sin(ωx+φ)(ω>0,0≤φ≤∏)为偶函数,其图像上的两个个最高点之间的距离为2π(1)求f(X)的解析式(2)若α∈(-π/3,π/2),f(α+π/3)=1/3,求sin(2α+5π/3)的值
根据最高点之间的距离为2π得T=2π,ω=1根据偶函数φ=π/2
f(x)=sin(x+π/2)
sin(2α+5π/3)=-cos(2α+2π/3)=-cos[2(α+π/3)]=然后用倍角公式
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