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已知函数 F(x)=Cos2x+2 3 sinxCosx(x∈...

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(法一)f(x)=3×1+c0s2x2+12sin2x?32=12sin2x+32cos2x=sin(2x+π3)(I )f(π4)=sin(2×π4+π3 )=cosπ3=12(II)函数的基本性质如下①奇偶性:函数f(x)既不是奇函数,也不是偶函数②单调性:函数f(x)的单调增区间为[kπ?5π12,kπ+π12] k∈Z,单...

(Ⅰ)f(x)=3cos2x+2sin(3π2+x)sin(π-x)=3cos2x-2cosxsinx=3cos2x-sin2x=2(32cos2x-12sin2x)=2cos(2x+π6),∴T=2π2=π,令2x+π6=kπ(k∈Z),即x=kπ2-π12(k∈Z),∴函数f(x)的对称轴方程为x=kπ2-π12(k∈Z),(Ⅱ)∵f(x)=2cos(2x+π6)...

(1)化简可得y=sin2x+2sinxcosx+3cos2x=1?cos2x2+sin2x+3×1+cos2x2=sin2x+cos2x+2=2sin(2x+π4)+2,∴f(x)周期T=2π2=π;(2)当2x+π4=2kπ+π2,即x=kπ+π8,k∈Z时,函数取最大值2+2,∴f(x)的最大值为2+2,取得最大值时x的集合为{x|x=kπ+π8,k...

f(x)=sin²x+2sinxcosx+3cos²x =(1-cos2x)/2+sin2x+3(1+cos2x)/2 =√2sin(2x+π/4)+2 (I) 函数f(x) 的最小正周期T=2π/2=π ∵x∈(0,π) ∴2x+π/4∈(π/4,9π/4) 当2x+π/4=π/2.即x=π/x时,f(x)=2+√2为最大值, 当2x+π/4=3π/2.即x=5π/8时,f(x)...

f(x)= - √3sin^2(x)+sinxcosx = -√3[(1-cos2x)/2]+(1/2)sinxcosx =(1/2)sin2x+(√3/2)cos2x-(√3/2) =sin2xcos60º+cos2xsin60º - (√3/2) f(x)=sin(2x+60º)-(√3/2) f(x/2)=sin[2(x/2)+60º] - (√3/2) =sin(x+60º) - (√3/2)...

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(...

(I)f(x)=sin2x-3cos2x+1=2sin(2x-π3)+1,∵ω=2,∴T=π;(II)∵x∈[π4,π2],2x-π3∈[π6,2π3],∴sin(2x-π3)∈[12,1],即2sin(2x-π3)+1∈[2,3],则函数f(x)的最大值为3,最小值为2.

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

(1)f(x)=cos2x+3sinxcosx+2sinxcos(x+π6)=cosx(cosx+3sinx)+2sinxcos(x+π6)=2cosxsin(x+π6)+2sinxcos(x+π6)=2sin(2x+π6)x∈[0,π2]时,2x+π6∈[π6,7π6],,sin(2x+π6)∈[?12,1],∴函数f(x)的值域是[-1,2](2)由|f(x)-k|<3得k-3<f(x)...

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