已知函数f(x)=sin(2x+π/3)-根号3cos(2x+π/3)写出f(x)单调区间 求f(x)在(-π/6,π/3)上的值域

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已知函数f(x)=sin(2x+π/3)-根号3cos(2x+π/3)写出f(x)单调区间求f(x)在(-π/6,π/3)上的值域已知函数f(x)=sin(2x+π/3)-根号3cos(2x+π/3)

已知函数f(x)=sin(2x+π/3)-根号3cos(2x+π/3)写出f(x)单调区间 求f(x)在(-π/6,π/3)上的值域
已知函数f(x)=sin(2x+π/3)-根号3cos(2x+π/3)写出f(x)单调区间 求f(x)在(-π/6,π/3)上的值域

已知函数f(x)=sin(2x+π/3)-根号3cos(2x+π/3)写出f(x)单调区间 求f(x)在(-π/6,π/3)上的值域
解由f(x)=sin(2x+π/3)-√3cos(2x+π/3)
=2(1/2sin(2x+π/3)-√3/2cos(2x+π/3))
=2sin(2x+π/3-π/3)
=2sin2x
知当2kπ-π/2≤2x≤2kπ+π/2,k属于Z,y是增函数
即当kπ-π/4≤x≤kπ+π/4,k属于Z,y是增函数
故函数的增区间为[kπ-π/4,kπ+π/4],k属于Z.
知当2kπ+π/2≤2x≤2kπ+3π/2,k属于Z,y是减函数
即当kπ+π/4≤x≤kπ+3π/8,k属于Z,y是减函数
故函数的减区间为[kπ+π/4,kπ+3π/8],k属于Z.
由x属于(-π/6,π/3)
知2x属于(-π/3,2π/3)
即sin2x属于(-√3/2,1]
即2sin2x属于(-√3,2]
故函数
f(x)在(-π/6,π/3)上的值域(-√3,2].