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)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/17 01:44:26

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)
（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

（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

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