已知向量a=(2,cosx),b=(sin(x+π/6),2),函数f(x)=a*b(1)求其单调增区间(2)若f(x)=6/5求cos(2x-π/3)的值
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![已知向量a=(2,cosx),b=(sin(x+π/6),2),函数f(x)=a*b(1)求其单调增区间(2)若f(x)=6/5求cos(2x-π/3)的值](/uploads/image/z/10201103-71-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%282%2Ccosx%29%2Cb%3D%EF%BC%88sin%EF%BC%88x%2B%CF%80%2F6%29%2C2%29%2C%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Da%2Ab%EF%BC%881%EF%BC%89%E6%B1%82%E5%85%B6%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%EF%BC%882%EF%BC%89%E8%8B%A5f%EF%BC%88x%EF%BC%89%3D6%2F5%E6%B1%82cos%EF%BC%882x-%CF%80%2F3%EF%BC%89%E7%9A%84%E5%80%BC)
已知向量a=(2,cosx),b=(sin(x+π/6),2),函数f(x)=a*b(1)求其单调增区间(2)若f(x)=6/5求cos(2x-π/3)的值
已知向量a=(2,cosx),b=(sin(x+π/6),2),函数f(x)=a*b
(1)求其单调增区间(2)若f(x)=6/5求cos(2x-π/3)的值
已知向量a=(2,cosx),b=(sin(x+π/6),2),函数f(x)=a*b(1)求其单调增区间(2)若f(x)=6/5求cos(2x-π/3)的值
(1) f(x)=a*b=2sin(x+π/6)+2cosx=√3sinx+3cosx
化成同名函数 f(x)= 2√3sin(x+π/6) (提取系数平方和)
则2kπ-π/2≤x+π/6≤2kπ+π/2
解得 f(x)的单调递增区间是[2kπ-2π/3,2kπ+π/3],k∈Z.
(2) f(x)= 2√3sin(x+π/6)=6/5
解得 sin(x+π/6)=√3/5
cos(2x-π/3) = cos(2x+π/6)
[sin(x/2)]^2=(1-cosx)/2
cos(2x-π/3)=16/25