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设函数F(x)=2根号3sinxCosx+2Cos^2x+m(1)求函数F...

f(x)=根号3sin2x+cos2x=2sin(2x+π/6) 1) T=2π/2=π x∈[0,π/2] 2x+π/6[π/6,7π/6] f(x)小=2sin(π/6)=1 f(x)大=2sin(π/2)=2 2) sin(2x0+π/6)=3/5 co2x0=cos(2x0+π/6-π/6)=(3-4根号3)/10 字限制

解: (1) f(x)=cos²x-√3sinxcosx+½ =½[1+cos(2x)]-(√3/2)sin(2x)+½ =½cos(2x)-(√3/2)sin(2x)+1 =cos(2x+π/3)+1 最小正周期T=2π/2=π cos(2x+π/3)=1时,f(x)取得最大值f(x)max=1+1=2 cos(2x+π/3)=-1时,f(x)取得最小值f(...

f(x)=2根号3sinxcosx+2cos^2x-1 =√3 sin2x+cos2x =2sin(2x+π/6) f(A)=2sin(2A+π/6)=2/3 sin(2A+π/6)=1/3 0

解1f(x)=cos2x+√3×2sinxcosx =cos2x+√3sin2x =2(1/2cos2x+√3/2sin2x) =2sin(2x+π/6) 故T=2π/2=π 当2kπ-π/2≤2x+π/6≤2kπ+π/2,k属于Z时,y是增函数。 即2kπ-2π/3≤2x≤2kπ+π/3,k属于Z时,y是增函数。 即kπ-π/3≤x≤kπ+π/6,k属于Z时,y是增函数。 故函数...

见图片吧

f(x)=1/2*根号3*2sinxcosx+(1-cos2x)/2=根号3/2sin2x-1/2cos2x+1=sin(2x+π/6)+1 1、T=2π/2=π +kπ f(x)∈{0,2} 2x+π/6∈{-π/2+2kπ,π/2+2kπ} y单增 x∈{-π/3+kπ,π/6+kπ} y单增 2、 x∈{π/2,π} 2x+π/6∈{π/6+π,π+2π} sin(2x+π/6)∈{-1/2,1} f(x)最大值是2...

求采纳,

f(x)=2√3sinxcosx+1-2(sinx)^2 =√3sin2x+cos2x =2sin(2x+π/6) 所以最小正周期=2π/2=π -π/2+2kπ

f(x)=sin^2x+√3sinxcosx+2cos^2x =cos^2x+√3/2*2sinxcosx+1 =1/2cos2x+√3/2sin2x+3/2 =sinx(2x+π/6)+3/2 T=2π/2=π 2x+π/6在[2kπ-π/2,2kπ+π/2]上单调递增 x在[kπ-5π/12,kπ+π/6]上单调递增 2)y=sin2x的图像经X轴向左平移π/12个单位得到y=sinx(2x+...

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