Question

已知函数f(x)已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)

Answer 1

（1）f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π) 即f(x)=√3sin(x+π/2)+sinx, f(x)=√3cosx+sinx f(x)=2（cosxsinπ/3+sinxcosπ/3) f(x)=2sin(x+π/3) 所以f(x)的最小正周期为T=2π. （2）因为f(x)的图像向右平移派/6个单位,得到函数g(x)的图像,则g(x)=2sin(x+π/3-π/6)=2sin(x+π/6), 由于π/6≦x+π/6≦7π/6 故当x=π时,g(x)最小,此时为g(π)=-1 ,当x=π/3时,g(x)最大,此时为g(π)=2