已知函数f(x)=2√3sin(x/2+派/4)cos(x/2+派/4)-sin(x+派)
问题描述:
已知函数f(x)=2√3sin(x/2+派/4)cos(x/2+派/4)-sin(x+派)
(1)求f(x)的最小正周期(2)若将f(x)的图像向右平移派/6个单位,得到函数g(x)的图像,求函数g(x)在区间[0,派]上的最大值和最小值
答
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
=√3cosx+sinx
=2sin(x+ π/3),
(1)2π.
(2)g(x)=2sin(x+π/6),在[0,π]上的最大值是2,最小值是-1.