y=sin^2x-3sinxcosx+2cos^2x
=1-3/2sin2x+cos^2x
=3/2-3/2sin2x+1/2cos2x
=√10/2cos(2x+t)+3/2
故函数y=sin^2x-3sinxcosx+2cos^2x的最小正周期为2π/2=π