已知函数f（x)=2sin^2x+2根号3sinx - 知识问答

已知函数f（x)=2sin^2x+2根号3sinxcosx+1,求f(x)的最小正周期,单调区间,最值

1个回答

f(x)=2(1-cos2x)/2+√3(sin2x)+1
=√3sin2x-cos2x+2
=2sin2xcosπ/6-2cos2xsinπ/6+2
=2(sin2xcosπ/6-cos2xsinπ/6)+2
=2sin(2x-π/6)+2
所以T=2π/2=π
增函数时2kπ-π/2

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