y=sin^x+根号3sinx*cosx的最小正周期和单调区间
问题描述:
y=sin^x+根号3sinx*cosx的最小正周期和单调区间
答
y = sin²x + √3sinxcosx
= (1 - cos2x)/2 + (√3/2)sin2x
= (√3/2)sin2x - (1/2)cos2x + 1/2
= sin(2x - π/6) + 1/2
蕞小正周期:2π/2 = π
2kπ - π/2 kπ - π/6 单增区间:(kπ - π/6,kπ + π/3),k∈Z
2kπ + π/2 kπ + π/3 单减区间:(kπ + π/3,kπ + 5π/6),k∈Z