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F(x)=sinx^4+2倍根号3 sinxCosx%Cosx^4 求(1)函...

f(x)=√3sinxcosx-cos²x-1/2 =(√3/2)sin2x-(1+cos2x)/2-1/2 =(√3/2)sin2x-(1/2)cos2x-1 =sin(2x-π/6)-1. 早小正周期T=2π/2=π. sin(2x-π/6)=-1, 即x=kπ-π/6时, 最小值f(x)|min=-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(...

f(x)=3cosx+4sinx =5×(3/5×cosx+4/5×sinx) =5×(sina×cosx+cosa×sinx),sina=3/5,cosa=4/5 =5sin(x+a) ∵-1≤sin(x+a)≤1 ∴-5≤sin(x+a)≤5 故,函数的值域为[-5,5]。 答题不易,望采纳~~~

max=3/2,min=1 解: f(x) =sin²x+√3sinxcosx =(1-cos2x)/2+(√3/2)sin2x =sin(2x-π/6)+1/2 ∵x∈[π/4,π/2] ∴2x-π/6∈[π/3,5π/6] ∴ f(x)_max=1+1/2=3/2 f(x)_min=1/2+1/2=1

f(x) = sinx^4+cos^2x = sinx^4+1-sin^2x = 1-sin^2x(1-sin^2x) = 1 - sin^2xcos^2x = 1- (sinxcosx)^2 = 1- (1/2sin2x)^2 = 1- 1/4 sin^2(2x) = 1 - 1/4 * (1-cos4x)/2 = 1/8 cos4x + 7/8 最小正周期 = 2π/4 = π/2 F(X) = sin^4x + 2√3sinxcosx...

(1)f(x)=2cosx(√3sinx+cosx)-1 =2√3sinxcosx+2(cosx)^2-1 =√3sin2x+cos2x =2sin(2x+π/6), x∈[0,π/2], u=2x+π/6的值域是[π/6,7π/6], v=sinu的值域是[-1/2,1], ∴f(x)=2v的最大值=2,最小值=-1. (2)f(x0)=2sin(2x0+π/6)=6/5, ∴sin(2x0+π/6)=3/5...

解: f(x)=2√3sinxcosx+1 -2sin²x =√3sin(2x)+cos(2x) =2[(√3/2)sin(2x)+(1/2)cos(2x)] =2sin(2x+π/6) -1≤sin(2x+π/6)≤1 -2≤2sin(2x+π/6)≤2 -2≤f(x)≤2 函数的值域为[-2,2]

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、先将f(x)=m*n化成一个函数式子,f(x)=m*n=√3sinxcosx/16+cosx/4,根据二倍角公式,等于三十二分之根号三倍的sin2x加上八分之cos2x加上1,。并进行提取公因式得到十六分之一倍的括号里二分之根号三倍的sin2x加上二分之cos2x括号结束再加上一,...

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