求下列函数的最大值,最小值,并求最小正周期 （1）y=1/2sinx+√3/2cosx (2)y=2sinx－2cosx
问题描述：
求下列函数的最大值,最小值,并求最小正周期 （1）y=1/2sinx+√3/2cosx (2)y=2sinx－2cosx
答
(1)
y=(1/2)sinx +(√3/2)cosx
=sinxcos(π/3)+cosxsin(π/3)
=sin(x+π/3)
sin(x+π/3)=1时,ymax=1
sin(x+π/3)=-1时,ymin=-1
2π/1=2π,最小正周期2π.
(2)
y=2sinx-2cosx
=2√2[(√2/2)sinx-(√2/2)cosx]
=2√2[sinxcos(π/4)-cosxsin(π/4)]
=2√2sin(x-π/4)
sin(x-π/4)=1时,ymax=2√2
sin(x-π/4)=-1时,ymin=-2√2
2π/1=2π,最小正周期2π.