已知函数f(x)=根号三cos²x+sinxcosx-根号三/2(1)求f(x)的最小正周期(2)求f(x)的单调递增区间
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![已知函数f(x)=根号三cos²x+sinxcosx-根号三/2(1)求f(x)的最小正周期(2)求f(x)的单调递增区间](/uploads/image/z/8903729-65-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%E6%A0%B9%E5%8F%B7%E4%B8%89cos%26%23178%3Bx%2Bsinxcosx-%E6%A0%B9%E5%8F%B7%E4%B8%89%2F2%EF%BC%881%EF%BC%89%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%9F%EF%BC%882%EF%BC%89%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4)
已知函数f(x)=根号三cos²x+sinxcosx-根号三/2(1)求f(x)的最小正周期(2)求f(x)的单调递增区间
已知函数f(x)=根号三cos²x+sinxcosx-根号三/2
(1)求f(x)的最小正周期
(2)求f(x)的单调递增区间
已知函数f(x)=根号三cos²x+sinxcosx-根号三/2(1)求f(x)的最小正周期(2)求f(x)的单调递增区间
f(x)=√3cos²x+sinxcosx-√3/2
=√3(cos2x+1)/2+sin2x /2-√3/2
=√3/2cos2x+√3/2+1/2sin2x -√3/2
=1/2sin2x+√3/2cos2x
=sin(2x+π/3)
(1)最小正周期为
T=2π/w=2π/2=π
(2)单调递增区间
2kπ-π/2≤2x+π/3≤2kπ+π/2 (k∈Z)
2kπ-π/2-π/3≤2x≤2kπ+π/2-π/3
2kπ-5π/6≤2x≤2kπ+π/6
kπ-5π/12≤x≤kπ+π/12
即单调递增区间为[kπ-5π/12,kπ+π/12] (k∈Z)