求f(x)=-cos²x+根号3sinxcosx的最小正周期和单调增区间
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![求f(x)=-cos²x+根号3sinxcosx的最小正周期和单调增区间](/uploads/image/z/5158423-55-3.jpg?t=%E6%B1%82f%28x%29%3D-cos%26%23178%3Bx%2B%E6%A0%B9%E5%8F%B73sinxcosx%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%92%8C%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4)
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求f(x)=-cos²x+根号3sinxcosx的最小正周期和单调增区间
求f(x)=-cos²x+根号3sinxcosx的最小正周期和单调增区间
求f(x)=-cos²x+根号3sinxcosx的最小正周期和单调增区间
f(x)=-cos²x+√3sinxcosx
=-1/2(1+cos2x)+√3/2sin2x
=√3/2sin2x-1/2cos2x-1/2
=sin(2x-π/6)-1/2
f(x)最小正周期T=2π/2=π
由2kπ-π/2≤2x-π/6≤2kπ+π/2,k∈Z
得kπ-π/6≤x≤kπ+π/3,k∈Z
f(x)递增区间为[kπ-π/6,kπ+π/3],k∈Z
由2kπ+π/2≤2x-π/6≤2kπ+3π/2,k∈Z
得kπ+π/3≤x≤kπ+5π/6,k∈Z
f(x)递减区间为[kπ+π/3,kπ+5π/6],k∈Z