化简 y=sin(π/6-2x)cos(π/6+2x) 并求周期及单调递减区间.
问题描述:
化简 y=sin(π/6-2x)cos(π/6+2x) 并求周期及单调递减区间.
答
y=-sin(2x-π/6)cos(2x+π/6)=-(1/2)[sin4x+sin(-π/3)]=-(1/2)sin4x+(√3/4)周期是T=π/2,减区间是2kπ-π/2≤4x≤2kπ+π/2,即:(kπ)/2-(π/8)≤x≤(kπ)/2+(π/8),则减区间是:[(kπ)/2-(π/8),(k...