y=(sinx)^2 +3(cosx)^2 +2sinxcosx
=2+2(cosx)^2+2sinxcosx
=2+cos2x+1+sin2x
=3+sin2x+cos2x
=√2sin(2x+π/4) + 3
最大值为3+√2
最小值为3-√2
最小正周期为 2π/2=π