已知函数f(x)=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2) 求值域 若函数图像与直线Y=-1有两个相邻交点间的距离为π/2,求Y=f(x)的单调递增区间?
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![已知函数f(x)=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2) 求值域 若函数图像与直线Y=-1有两个相邻交点间的距离为π/2,求Y=f(x)的单调递增区间?](/uploads/image/z/3860116-52-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28wx%2B%CF%80%2F6%29%2Bsin%28wx-6%2F%CF%80%29-2cos%5E2%28wx%2F2%29+%E6%B1%82%E5%80%BC%E5%9F%9F+%E8%8B%A5%E5%87%BD%E6%95%B0%E5%9B%BE%E5%83%8F%E4%B8%8E%E7%9B%B4%E7%BA%BFY%3D-1%E6%9C%89%E4%B8%A4%E4%B8%AA%E7%9B%B8%E9%82%BB%E4%BA%A4%E7%82%B9%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%CF%80%2F2%2C%E6%B1%82Y%3Df%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4%3F)
已知函数f(x)=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2) 求值域 若函数图像与直线Y=-1有两个相邻交点间的距离为π/2,求Y=f(x)的单调递增区间?
已知函数f(x)=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2) 求值域 若函数图像与直线Y=-1有两个相邻交点间的
距离为π/2,求Y=f(x)的单调递增区间?
已知函数f(x)=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2) 求值域 若函数图像与直线Y=-1有两个相邻交点间的距离为π/2,求Y=f(x)的单调递增区间?
f(x)
=sin(wx+π/6)+sin(wx-6/π)-2cos^2(wx/2)
=sin(wx)* √3/2+cow(wx)*1/2+sin(wx)*√3/2-cos(wx)*1/2-(cos(wx)+1)
=sin(wx)*√3-cos(wx)-1
=2*sin(wx-π/6)-1
所以
-3≤f(x)≤1
f(x)=-1时,sin(wx-π/6)=0,x=(n+1/6)π/w
间距π/2,所以w=2
所以f(x)=2sin(2x-π/6)-1
单调递增区间为:2nπ-1/2π ≤ 2x-π/6 ≤ 2nπ+1/2π
所以 nπ-1/6π ≤ x ≤ nπ+1/3π
f(x)=2sinwx cosπ/6-1-coswx
=2(sinwx cosπ/6- coswx sinπ/6)-1
=2sin(wx-π/6)-1
f max=1,f min=-3
值域[-3,1]
f(x)=2sin(2x-π/6)-1
kπ+π/2=2x-π/6
2x= kπ+2π/3
对称轴方程x= kπ/2+π/3,k∈Z