y=√3sinxcosx+cos²x+1的最小正周期和单调区间

问题描述:

y=√3sinxcosx+cos²x+1的最小正周期和单调区间

y=(√3/2)sin2x+(1/2)cos2x+(1/2)=sin(2x+π/6)+(1/2)
1、最小正周期T=2π/2=π;
2、增区间:2kπ-π/2≤2x+π/6≤2kπ+π/2,得:kπ-π/3≤x≤kπ+π/6
即增区间是[2kπ-π/3,2kπ+π/6],其中k∈Z
减区间:2kπ+π/2≤2x+π/6≤2kπ+3π/2,得:kπ+π/6≤x≤k+2π/3
即减区间是[kπ+π/6,kπ+2π/3],其中k∈Z