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已知函数F(x)=根号3sinx%Cosx,x属于R,若F(x)大于...

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+...

f(x)=√3sinxcosx+cos²x =(√3/2)·2sinxcosx+½(2cos²x-1)+½ =(√3/2)sin2x+½cos2x+½ =sin(2x+π/6) +½ 最小正周期T=2π/2=π

1:∵函数f(x) =√3sinxcosx-(cosx)^2-1/2 =cosx(√3sinx-cosx)-1/2=2cosxsin(x-π/6)-1/2 =sin(2x-π/6)-sin(π/6)-1/2 =sin(2x-π/6)-1 ∴f(x)的最小值为-2,最小正周期为π 2。f(C)=sin(2c-π/6)-1=0 则sin(2c-π/6)=1 当2c-π/6=π/2时。f(c)=0求...

(sinx-cosx)sinx =(sinx)^2-sinxcosx =[-1+2(sinx)^2]/2+1/2-(sin2x)/2 =(-1/2)(cos2x+sin2x)+1/2 =(-√2/2)sin(2x+φ)+1/2 =(-√2/2)sin[2(x+φ/2)]+1/2 ∴最小正周期是(2π)/2=π

求采纳,

f(x)=根号下3sinx×cosx–cos²x–½ =(根3)/2*sin2x-1/2*(cos2x+1)-1/2 =(根3)/2*sin2x-1/2*cos2x-1 =sin(2x-pi/6)-1

见图

解 f(x)=√3cos²x+sinxcosx-√3/2 =√3*(1+cos2x)/2+(1/2)sin2x-√3/2 =(1/2)sin2x+(√3/2)cos2x =sin(2x+π/3) ∴T=π 单增区间: -π/2+2kπ≤2x+π/3≤π/2+2kπ,k∈Z -5π/6+2kπ≤2x≤π/6+2kπ,k∈Z -5π/12+kπ≤x≤π/12+2kπ,k∈Z 即为:[-π/12+kπ,5π/12+kπ],k∈Z

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