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已知函数F(x)=23sinxCosx+2Cos2x%1(x∈R),g(x...

(1)由f(x)=23sinxcosx+2cos2x-1,得f(x)=3(2sinxcosx)+(2cos2x-1)=3sin2x+cos2x=2sin(2x+π6),所以函数f(x)的最小正周期为π.(2)因为f(x)=2sin(2x+π6)在区间[0,π6]上为增函数,在区间[π6,π2]上为减函数,又f(0)=1,f(π...

(1)f(x)=32sin2x-12cos2x=sin(2x-π6),∵ω=2,∴f(x)的最小正周期T=2π2=π,令2x-π6=kπ+π2,得到x=kπ2+π3(k∈Z),则图象的对称轴方程为x=kπ2+π3(k∈Z);(2)要得到函数g(x)=sinx的图象,只需将函数f(x)的图象首先向左平移π12,得到y...

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)=3sin2x?3sin2x?cos2x+2(sin2x+cos2x)=3sin2x+cos2x?sin2x=3sin2x+cos2x=2sin(2x+π6)∴f(x)的最大值是2.(Ⅱ)由条件得 sin(2A+C)=2sinA+2sinAcos(A+C),∴sinAcos(A+C)+cosAsin(A+C)=2sinA+2sinAcos(A+C),化简得 sinC=...

1)f(x)=cos²x=(1+cos2x)/2, 对称轴为x=kπ/2 故有a=kπ/2, k为任意整数 g(2a)=1/2+√3sin(kπ)cos(kπ)=1/2 2) h(x)=(1+cos2x)/2+1/2+√3/2sin2x=1+sin(2x+π/6) 最大值为1+1=2 最小值为1-1=0 h(x)的值域为[0, 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

f(x)=cos2x+2sinxcosx+1 =cos2x+sin2x+1 =√2(√2/2*cos2x+√2/2*sin2x)+1 =√2cos(2x-π/4)+1 ∵-1≤cos(2x-π/4)≤1 ∴1-√2≤√2cos(2x-π/4)+1≤1+√2 则f(x)值域为:[1-√2,1+√2] 行家解答,质量保证

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

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