f(x)=-sin2x+2倍根号3sin²x-根号3+1,求最小正周期和单减区间

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f(x)=-sin2x+2倍根号3sin²x-根号3+1,求最小正周期和单减区间
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f(x)=-sin2x+2倍根号3sin²x-根号3+1,求最小正周期和单减区间
f(x)=-sin2x+2倍根号3sin²x-根号3+1,求最小正周期和单减区间

f(x)=-sin2x+2倍根号3sin²x-根号3+1,求最小正周期和单减区间
f(x)=-sin(2x)+2√3sin²x -√3+1
=-sin(2x)+√3[1-cos(2x)] -√3+1
=-sin(2x)-√3cos(2x) +1
=(-2)[(1/2)sin(2x)+(√3/2)cos(2x)] +1
=(-2)sin(2x+π/3) +1
最小正周期Tmin=2π/2=π
sin(2x+π/3)单调递增时,-2sin(2x+π/3)单调递减,f(x)单调递减.此时
2kπ-π/2≤2x+π/3≤2kπ+π/2 (k∈Z)
kπ-5π/12≤x≤kπ+π/12 (k∈Z)
函数的单调递减区间为[kπ-5π/12,kπ+π/12] (k∈Z)