已知函数f(x)=sin2xcosfai-2cos^2xsin(x-fai)-cos(π/2+fai)(-π/2<fai<π/2)在x=π/6时取得最大值.求fai的值将函数y=f(x)图象上各点的横坐标扩大到原来的2倍,纵坐标不变,得到函数y=g(x)的图象,若g(α)=1/3,α
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![已知函数f(x)=sin2xcosfai-2cos^2xsin(x-fai)-cos(π/2+fai)(-π/2<fai<π/2)在x=π/6时取得最大值.求fai的值将函数y=f(x)图象上各点的横坐标扩大到原来的2倍,纵坐标不变,得到函数y=g(x)的图象,若g(α)=1/3,α](/uploads/image/z/8562305-65-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin2xcosfai-2cos%5E2xsin%28x-fai%29-cos%28%CF%80%2F2%2Bfai%29%EF%BC%88-%CF%80%2F2%EF%BC%9Cfai%EF%BC%9C%CF%80%2F2%EF%BC%89%E5%9C%A8x%3D%CF%80%2F6%E6%97%B6%E5%8F%96%E5%BE%97%E6%9C%80%E5%A4%A7%E5%80%BC.%E6%B1%82fai%E7%9A%84%E5%80%BC%E5%B0%86%E5%87%BD%E6%95%B0y%3Df%28x%29%E5%9B%BE%E8%B1%A1%E4%B8%8A%E5%90%84%E7%82%B9%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E6%89%A9%E5%A4%A7%E5%88%B0%E5%8E%9F%E6%9D%A5%E7%9A%842%E5%80%8D%2C%E7%BA%B5%E5%9D%90%E6%A0%87%E4%B8%8D%E5%8F%98%2C%E5%BE%97%E5%88%B0%E5%87%BD%E6%95%B0y%3Dg%28x%29%E7%9A%84%E5%9B%BE%E8%B1%A1%2C%E8%8B%A5g%28%CE%B1%29%3D1%2F3%2C%CE%B1)
已知函数f(x)=sin2xcosfai-2cos^2xsin(x-fai)-cos(π/2+fai)(-π/2<fai<π/2)在x=π/6时取得最大值.求fai的值将函数y=f(x)图象上各点的横坐标扩大到原来的2倍,纵坐标不变,得到函数y=g(x)的图象,若g(α)=1/3,α
已知函数f(x)=sin2xcosfai-2cos^2xsin(x-fai)-cos(π/2+fai)(-π/2<fai<π/2)在x=π/6时取得最大值.
求fai的值
将函数y=f(x)图象上各点的横坐标扩大到原来的2倍,纵坐标不变,得到函数y=g(x)的图象,若g(α)=1/3,α∈(-π/2,0),求cosα的值
已知函数f(x)=sin2xcosfai-2cos^2xsin(x-fai)-cos(π/2+fai)(-π/2<fai<π/2)在x=π/6时取得最大值.求fai的值将函数y=f(x)图象上各点的横坐标扩大到原来的2倍,纵坐标不变,得到函数y=g(x)的图象,若g(α)=1/3,α
题出错了sin(π-φ)-否则没法算
f(x)=sin2xcosφ-2cos^2xsin(π-φ)-cos(π/2+φ)(-π/2<φ<π/2)
=sin2xcosφ-sinφ(2cos^2x-1)
=sin2xcosφ-cos2xsinφ
=sin(2x-φ)
x=π/6时取得最大值(-π/2<φ<π/2)
π/3-φ=π/2+2kπ,k是整数
φ=-π/6
g(x)=sin(x+π/6)
cos(a)=sin(a+π/6)=1/3
α∈(-π/2,0)
α+π/6∈(-π/3,π/6)
cos(α+π/6)=√(1-1/9)=2√2/3
cosα=cos((α+π/6)-α)
=cos(α+π/6)cosπ/6+sin(α+π/6)sinπ/6
=(2√6+1)/6