【50分】函数f(x)=sin^2(x/2)+√3sin(x/2)cos(x/2)-1/2,求单调区间!

题目

【50分】函数f(x)=sin^2(x/2)+√3sin(x/2)cos(x/2)-1/2,求单调区间!

答案

f(x)=sin^2(x/2)+√3sin(x/2)cos(x/2)-1/2=(1/2)(1-cosx)+(√3/2)sinx-1/2=(√3/2)sinx-(1/2)cosx=sinxcos30°-cosxsin30°=sin(x-30°)=sin(x-π/6）由2kπ-π/2≤x-π/6≤2kπ+π/2得2kπ-π/3≤x≤2kπ+2π/3 [2k...