(1)
y=(1/2)sinx +(√3/2)cosx
=sinxcos(π/3)+cosxsin(π/3)
=sin(x+π/3)
sin(x+π/3)=1時(shí),ymax=1
sin(x+π/3)=-1時(shí),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時(shí),ymax=2√2
sin(x-π/4)=-1時(shí),ymin=-2√2
2π/1=2π,最小正周期2π.