设向量a=(sinx,cosx),b=(sinx,√3sinx),x属于R,函数f(x)=a(a+2b).设向量a=(sinx,cosx),b=(sinx,根号3sinx),x属于R,函数f(x)=a(a+2b).1,求f(x)的最小正周期T2,已知a,b,c分别为△ABC的内角A,B.C,的对边,其中A为锐角,a=√3,
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![设向量a=(sinx,cosx),b=(sinx,√3sinx),x属于R,函数f(x)=a(a+2b).设向量a=(sinx,cosx),b=(sinx,根号3sinx),x属于R,函数f(x)=a(a+2b).1,求f(x)的最小正周期T2,已知a,b,c分别为△ABC的内角A,B.C,的对边,其中A为锐角,a=√3,](/uploads/image/z/12583790-62-0.jpg?t=%E8%AE%BE%E5%90%91%E9%87%8Fa%3D%28sinx%2Ccosx%29%2Cb%3D%28sinx%2C%E2%88%9A3sinx%29%2Cx%E5%B1%9E%E4%BA%8ER%2C%E5%87%BD%E6%95%B0f%28x%29%3Da%28a%2B2b%29.%E8%AE%BE%E5%90%91%E9%87%8Fa%3D%28sinx%2Ccosx%29%2Cb%3D%28sinx%2C%E6%A0%B9%E5%8F%B73sinx%29%2Cx%E5%B1%9E%E4%BA%8ER%2C%E5%87%BD%E6%95%B0f%28x%29%3Da%28a%2B2b%29.1%2C%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9FT2%2C%E5%B7%B2%E7%9F%A5a%2Cb%2Cc%E5%88%86%E5%88%AB%E4%B8%BA%E2%96%B3ABC%E7%9A%84%E5%86%85%E8%A7%92A%2CB.C%2C%E7%9A%84%E5%AF%B9%E8%BE%B9%2C%E5%85%B6%E4%B8%ADA%E4%B8%BA%E9%94%90%E8%A7%92%2Ca%3D%E2%88%9A3%2C)
设向量a=(sinx,cosx),b=(sinx,√3sinx),x属于R,函数f(x)=a(a+2b).设向量a=(sinx,cosx),b=(sinx,根号3sinx),x属于R,函数f(x)=a(a+2b).1,求f(x)的最小正周期T2,已知a,b,c分别为△ABC的内角A,B.C,的对边,其中A为锐角,a=√3,
设向量a=(sinx,cosx),b=(sinx,√3sinx),x属于R,函数f(x)=a(a+2b).
设向量a=(sinx,cosx),b=(sinx,根号3sinx),x属于R,函数f(x)=a(a+2b).
1,求f(x)的最小正周期T
2,已知a,b,c分别为△ABC的内角A,B.C,的对边,其中A为锐角,a=√3,c=2,且f(A)恰好是F(x)在[0,二分之派]上的最大值,求角A和边b的值
设向量a=(sinx,cosx),b=(sinx,√3sinx),x属于R,函数f(x)=a(a+2b).设向量a=(sinx,cosx),b=(sinx,根号3sinx),x属于R,函数f(x)=a(a+2b).1,求f(x)的最小正周期T2,已知a,b,c分别为△ABC的内角A,B.C,的对边,其中A为锐角,a=√3,
a+2b=(3sinx,cosx+2√3sinx)
∴f(x)=(sinx,cosx)(3sinx,cosx+2√3sinx)
=3sin²x+cos²x+2√3sinxcosx
=1+2sin²x+2√3sinxcosx
=1+1-cos2x+√3sin2x
=2+√3sin2x-cos2x
=2+2sin(2x-π/6)
∴f(x)的最小正周期T=2π/2=π
x∈[0,π/2]时,-π/6≤2x-π/6≤5π/6
∴sin(2x-π/6)≤1,当x=π/3时,取到最大值
∴f(x)在[0,π/2]上最大值为4,此时x=π/3
∴A=π/3
又余弦定理a²=b²+c²-2bccosA
∴3=b²-2b+4 => b²-2b+1=0 => b=1
(1)由题意,f(x)=a(a+2b)=a²+2ab=sin²x+cos²x+2(sin²x+√3sinxcosx)=1+2sin²x+√3sin2x
=1+(1-cos2x)+√3sin2x=2+√3sin2x-cos2x=2+2sin(2x-π/6)
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(1)由题意,f(x)=a(a+2b)=a²+2ab=sin²x+cos²x+2(sin²x+√3sinxcosx)=1+2sin²x+√3sin2x
=1+(1-cos2x)+√3sin2x=2+√3sin2x-cos2x=2+2sin(2x-π/6)
则f(x)的最小正周期T为2π/2=π
(2)由(1)知,f(x)=2+2sin(2x-π/6)
当x∈[0,π/2]时,2x-π/6∈[-π/6,5π/6]
当且仅当2x-π/6=π/2时,即x=π/3时,f(x)取最大值,即A=π/3
由余弦定理得,sinA/a=sinC/c,则sin(π/3)/√3=sinC/2,解得C=π/2
则B=π-π/3-π/2=π/6
有勾股定理得(C为π/2),a²+b²=c²,则3+b²=4,b=1
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