已知函数f(x)=sin(wx+π/6)+cos(wx+π/6)(w>0)且函数y=f(x)图像的两相邻对称轴间距离为π/2求f(x)
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![已知函数f(x)=sin(wx+π/6)+cos(wx+π/6)(w>0)且函数y=f(x)图像的两相邻对称轴间距离为π/2求f(x)](/uploads/image/z/3857495-23-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28wx%2B%CF%80%2F6%29%2Bcos%28wx%2B%CF%80%2F6%29%28w%3E0%29%E4%B8%94%E5%87%BD%E6%95%B0y%3Df%28x%29%E5%9B%BE%E5%83%8F%E7%9A%84%E4%B8%A4%E7%9B%B8%E9%82%BB%E5%AF%B9%E7%A7%B0%E8%BD%B4%E9%97%B4%E8%B7%9D%E7%A6%BB%E4%B8%BA%CF%80%2F2%E6%B1%82f%28x%EF%BC%89)
已知函数f(x)=sin(wx+π/6)+cos(wx+π/6)(w>0)且函数y=f(x)图像的两相邻对称轴间距离为π/2求f(x)
已知函数f(x)=sin(wx+π/6)+cos(wx+π/6)(w>0)且函数y=f(x)图像的两相邻对称轴间距离为π/2求f(x)
已知函数f(x)=sin(wx+π/6)+cos(wx+π/6)(w>0)且函数y=f(x)图像的两相邻对称轴间距离为π/2求f(x)
sin(wx+π/6)+cos(wx+π/6) =根2[根2/2(sin(wx+π/6)+cos(wx+π/6))]=根2[sin(wx+π/6+π/4)]
可以看出x的系数为w
函数y=f(x)图像的两相邻对称轴间距离为π/2,即D=π/2 T=2D=π
T=2π/w=π
w=2
所以原式=根2[sin(2x+π/6+π/4)] =根2[sin(2x+5π/12)]
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