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F(x)=根号3sinx/4Cosx/4+Cosx/4的平方+1/2

、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,...

f(x)=m·n=√3sin(x/4)cos(x/4)+cos²(x/4) =(√3/2)sin(x/2)+(1/2)cos(x/2)+1/2 =sin(x/2+π/6)+1/2, 则f(A)=sin(A/2+π/6)+1/2, ∵(2a-c)cosB=bcosC, ∴(2sinA-sinC)cosB=sinBcosC, 2sinAcosB=sinBcosC+cosBsinC, 2sinAcosB=sin(B+C)=sin(π-A...

f(x)=1/2•(cos²x-sin²x)-2asinx+b =-sin²x-2asinx+b-1/2 =-(sinx-a)²+b-1/2+a²。 u=sinx, -1≤u≤1, f(x)=-(u-a)²+b-1/2+a² 转化为二次函数在动轴定区间上的值域问题。分类讨论01. 注意抛物线y=g(u)开...

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)=2sin(x/4)cos(x/4)+√3cos(x/2) =sin(x/2)+√3cos(x/2) =2cos(π/3)sin(x/2)+2sin(π/3)cos(x/2) =2sin(x/2+π/3), (1)最小正周期=4π. 最大值=2,最小值=-2.

天钰 原式可化简为f(x)=√6sin(x/2+π/6)≤m 可知-π/4≤(x/2+π/6)≤π/4 于是m≥√3

(1)由题意得:函数f(x)=3sinx4?cosx4+cos2x4=32sinx2+1+cosx22=sin(x2+π6)+12.…(3分)∵f(x)=1,即 sin(x2+π6)=12,则 cos(2π3-x)=2cos2(π3?x2)-1=2sin2(x2+π6)-1=-12. …(6分)(2)在△ABC中,由acosC+12c=b 可得 a?a2+b2?c22ab+...

f(x)=2√3sinxcosx+2cos²x =√3sin2x+cos2x+1 =2sin(2x+π/6)+1 f(4π/3)=2sin(8π/3+π/6)+1=2sin5π/6+1=2 x∈[0,π/2] 2x+π/6∈[π/6,2π/3] f(x)的值域:[2,3]

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