已知函数f(x)=sin^wx+根3sinwxcoswx(w>0)图像的两相邻对称轴间的距离为π/2.求w的值和f(x)的单调区间
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![已知函数f(x)=sin^wx+根3sinwxcoswx(w>0)图像的两相邻对称轴间的距离为π/2.求w的值和f(x)的单调区间](/uploads/image/z/14572618-34-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%5Ewx%2B%E6%A0%B93sinwxcoswx%28w%3E0%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%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%CF%80%2F2.%E6%B1%82w%E7%9A%84%E5%80%BC%E5%92%8Cf%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4)
已知函数f(x)=sin^wx+根3sinwxcoswx(w>0)图像的两相邻对称轴间的距离为π/2.求w的值和f(x)的单调区间
已知函数f(x)=sin^wx+根3sinwxcoswx(w>0)图像的两相邻对称轴间的距离为π/2.求w的值和f(x)的单调区间
已知函数f(x)=sin^wx+根3sinwxcoswx(w>0)图像的两相邻对称轴间的距离为π/2.求w的值和f(x)的单调区间
f(x)=(1/2)(1-cos2wx)+(√3/2)sin2wx=sin(2wx-π/6)+1/2,
它图像的两相邻对称轴间的距离为π/2=T/2=π/(2w),w=1.
f(x)=sin(2x-π/6)+1/2,
它的增区间由(2k-1/2)π<2x-π/6<(2k+1/2)π,k∈Z确定,
各加π/6,得(2k-1/3)π<2x<(2k+2/3)π,
各除以2,得(k-1/6)π
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