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3Cos2x sin2x

特征方程为r²+1=0,得r=i, -i 设特解为y*=acos2x+bsin2x y*'=-2asin2x+2bcos2x y*"=-4acos2x-4bsin2x 代入方程得:-4acos2x-4bsin2x+acos2x+bsin2x=3cos2x+sin2x -3acos2x-3bsinx=3cos2x+sin2x 比较系数得:-3a=3, -3b=1 得a=-1, b=-1/3 因...

如图

f(x)=sin2x+3cos2x=2(12sin2x+32cos2x)=2sin(2x+π3).∵f(x)的图象关于点(x0,0)成中心对称,∴f(x0)=0,即2sin(2x0+π3)=0,∴2x0+π3=kπ,x0=kπ2?π6,k∈Z,∵x0∈[0,π2],∴x0=π3.故选:C.

D

(1)f(X)=sin2X+√3cos2X=2(1/2sin2X+√3/2cos2X)=2(cosπ/3sin2x+sinπ/3cos2x) =2sin(2x+π/3) 即f(x)=2sin(2x+π/3) (2)∵-1≤sin(2x+π/3)≤1 ∴-2≤2sin(2x+π/3)≤2 ∴函数的最大值为2,最小值为-2 (3)最小正周期为T=2π/2=π (4)令2x+π/3=-π...

(1)∵y=sin2x+sin2x+3cos2x=sin2x+cos2x+2=2sin(2x+π4)+2,∴当2x+π4=2kπ-π2(k∈Z),即x=kπ-3π8(k∈Z)时,f(x)取得最小值2-2,即f(x)min=2-2,x的集合为{x|x=kπ-3π8,k∈Z}.(2)由2kπ+π2≤2x+π4≤2kπ+3π2(k∈Z)得:π8+kπ≤x≤5π8+kπ(k∈Z...

∵f(x)=sin2x-2sinxcosx+3cos2x=1-2sinxcosx+2cos2x=1+1+cos2x-sin2x=-(sin2x-cos2x)+2=-2sin(2x-π4)+2.∴把函数f(x)的图象沿x轴向左平移m(m>0)个单位,得到函数g(x)的图象的解析式为:g(x)=-2sin(2x+2m-π4)+2.∵函数g(x)的图象关...

用辅助角公式

f(x)=sin(2x+π/3)+√3/3sin2x-√3/3cos2x =1/2sin2x+√3/2cos2x+√3/3sin2x-√3/3cos2x =( 1/2+√3/3)sin2x+√3/6cos2x =√(2/3+√3/3)sin(2x+φ) tanφ=√3/6/( 1/2+√3/3)=2-√3 φ=π/12 ∴fx的最小正周期=2π/2=π sinx的对称轴:x=kπ+π/2 ∴2x+π/12=kπ+π/2 x=kπ...

f(x)=-sin2x+√3cos2x = 2(-1/2sin2x+√3/2cos2x) = 2{sin2xcos(-π/3)+cos2xsin(-π/3)} = 2sin(2x-π/3) f(x)=-sin2x+√3cos2x = 2(-1/2sin2x+√3/2cos2x) = 2{-sin2xsinπ/6+cos2xcosπ/6} = 2cos(2x+π/6)

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