设函数f(x)=向量a×(向量b+c),其中向量a=(sinx,-cosx),向量b=(sinx,-3cosx),向量c=(-cosx,sinx),x∈R.(1)【以求出函数解析式为fx=2+根号2×sin(2x+3π/4)】(2)求当x∈【3π/8,7π/8】时,函数f(x)的单
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![设函数f(x)=向量a×(向量b+c),其中向量a=(sinx,-cosx),向量b=(sinx,-3cosx),向量c=(-cosx,sinx),x∈R.(1)【以求出函数解析式为fx=2+根号2×sin(2x+3π/4)】(2)求当x∈【3π/8,7π/8】时,函数f(x)的单](/uploads/image/z/2625435-27-5.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D%E5%90%91%E9%87%8Fa%C3%97%28%E5%90%91%E9%87%8Fb%2Bc%29%2C%E5%85%B6%E4%B8%AD%E5%90%91%E9%87%8Fa%3D%28sinx%2C-cosx%29%2C%E5%90%91%E9%87%8Fb%3D%EF%BC%88sinx%2C-3cosx%EF%BC%89%2C%E5%90%91%E9%87%8Fc%3D%EF%BC%88-cosx%2Csinx%EF%BC%89%2Cx%E2%88%88R.%EF%BC%881%EF%BC%89%E3%80%90%E4%BB%A5%E6%B1%82%E5%87%BA%E5%87%BD%E6%95%B0%E8%A7%A3%E6%9E%90%E5%BC%8F%E4%B8%BAfx%3D2%2B%E6%A0%B9%E5%8F%B72%C3%97sin%EF%BC%882x%2B3%CF%80%2F4%EF%BC%89%E3%80%91%EF%BC%882%EF%BC%89%E6%B1%82%E5%BD%93x%E2%88%88%E3%80%903%CF%80%2F8%2C7%CF%80%2F8%E3%80%91%E6%97%B6%2C%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95)
设函数f(x)=向量a×(向量b+c),其中向量a=(sinx,-cosx),向量b=(sinx,-3cosx),向量c=(-cosx,sinx),x∈R.(1)【以求出函数解析式为fx=2+根号2×sin(2x+3π/4)】(2)求当x∈【3π/8,7π/8】时,函数f(x)的单
设函数f(x)=向量a×(向量b+c),其中向量a=(sinx,-cosx),向量b=(sinx,-3cosx),向量c=(-cosx,sinx)
,x∈R.
(1)【以求出函数解析式为fx=2+根号2×sin(2x+3π/4)】
(2)求当x∈【3π/8,7π/8】时,函数f(x)的单调性
(3)y=cosx的图像函数经过怎样的转换得到f(x)的图像
设函数f(x)=向量a×(向量b+c),其中向量a=(sinx,-cosx),向量b=(sinx,-3cosx),向量c=(-cosx,sinx),x∈R.(1)【以求出函数解析式为fx=2+根号2×sin(2x+3π/4)】(2)求当x∈【3π/8,7π/8】时,函数f(x)的单
(1)f(x)=a(b+c)=ab+ac=sinxsinx+3coxcox-2sinxcosx
=2cosxcosx-sin2x+1
=-sin2x+cos2x+2
=√2sin(2x+3π/4)+2
(2)当x属于[3π/8,7π/8]时,2x+3π/4属于[3π/2,5π/2]
根据sinx的性质得到f(x)在[3π/8,7π/8]单调递增
(3)先将y=cosx向右平移π/2个单位,得到y=cos(x-π/2)=sinx
再x不变,y增大√2倍,得到y=√2sinx
再y不变,x减小为原来的1/2,得到y=√2sin(2x)
再向左平移3π/8个单位,得到y=√2sin(2x+3π/4)
最后向上平移2个单位,得到y=√2sin(2x+3π/4)+2