Question

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

Answer 1

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.

Answer 2

f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3(2sin(x/2+π/4)cos(x/2+π/4))-sin(x+π)
=√3sin(x+π/2)-(-sinx)
=√3cosx+sinx
=2(sinπ/3cosx+cosπ/3sinx)
=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.