已知函数f(x)=sin(2x+π/6)+2sin^2(x+π/6)-2cos^2x+a-1
已知函数f(x)=sin(2x+π/6)+2sin^2(x+π/6)-2cos^2x+a-1
,1.求最小正周期
2.求f（x）的单调增区间
3 求f（x）的最大值及此时x值
4.若当x∈【0,2/派】时,f（x）的最小值为2,求a
,1.求最小正周期
2.求f（x）的单调增区间
3 求f（x）的最大值及此时x值
4.若当x∈【0,2/派】时,f（x）的最小值为2,求a
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f(x)=sin(2x+π/6)+2sin^2(x+π/6)-2cos^2x+a-1
=sin2xcosπ/6+cos2xsinπ/6-cos(2x+π/3)-cos2x+a-1
=(√3/2)sin2x+(1/2)cos2x-cos2xcosπ/3+sin2xsinπ/3-cos2x+a-1
=(√3/2)sin2x-(1/2)cos2x-(1/2)cos2x+(√3/2)sin2x+a-1
=2[(√3/2)sin2x-(1/2)cos2x]+a-1
=2(sin2xcosπ/6-cos2xsinπ/6)+a-1
=2sin(2x-π/6)+a-1
1.
最小正周期为T=2π/2=π
2.
2kπ-π/2
=sin2xcosπ/6+cos2xsinπ/6-cos(2x+π/3)-cos2x+a-1
=(√3/2)sin2x+(1/2)cos2x-cos2xcosπ/3+sin2xsinπ/3-cos2x+a-1
=(√3/2)sin2x-(1/2)cos2x-(1/2)cos2x+(√3/2)sin2x+a-1
=2[(√3/2)sin2x-(1/2)cos2x]+a-1
=2(sin2xcosπ/6-cos2xsinπ/6)+a-1
=2sin(2x-π/6)+a-1
1.
最小正周期为T=2π/2=π
2.
2kπ-π/2
1年前
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