已知函数f（x）=根号3sinxcosx-cos^2x-1/2 q求f(x)最小值和最小正周期

题目

已知函数f（x）=根号3sinxcosx-cos^2x-1/2 q求f(x)最小值和最小正周期

答案

f(x) = √3sinxcosx-cos^2x-1/2
= √3/2sin2x-(cos2x + 1)/2 - 1/2
= √3/2sin2x-1/2cos2x - 1
= sin2xcosπ/6-cos2xsinπ/6 - 1
= sin(2x-π/6) - 1
sin(2x-π/6) ≥-1
f(x) = sin(2x-π/6) - 1 ≥ -2,最小值-2
2π/2 = π,最小正周期π