f(x)=2sin(x/4)*cos(x/4)-2√3sin²(x/4)+√3(1)求最小正周期(2)求最值与取得最值时X的集合(3)对称中心对称轴
问题描述:
f(x)=2sin(x/4)*cos(x/4)-2√3sin²(x/4)+√3
(1)求最小正周期(2)求最值与取得最值时X的集合(3)对称中心对称轴
答
f(x)=2sin(x/4)*cos(x/4)-2√3sin²(x/4)+√3=sinx/2-√3(1-cosx/2)+√3=sinx/2-√3+√3cosx/2+√3=sinx/2+√3cosx/2=2(sinx/2cosπ/3+cosx/2sinπ/3)=2sin(x/2+π/3)最小正周期是 2π*2=4π当x/2+π/3=(2k+1/2)...