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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+...

函数f(x)=3sinx-cosx=2sin(x-π6),因为f(x)≥1,所以2sin(x-π6)≥1,所以,2kπ+π6≤x?π6≤2kπ+5π6 k∈Z所以f(x)≥1,则x的取值范围为:{x|2kπ+π3≤x≤2kπ+π,k∈Z}故选:B

求采纳,

(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

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...

利用向量点积的定义,然后利两角和的正弦公式进行化简。

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

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)=(1-cos2x)/2+√3/2sin2x+1+cos2x =√3/2sin2x+1/2cos2x+3/2 =sin(2x+π/6)+3/2 的最小正周期 T=2π/2=π 2kπ-π/2

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