y=sinxcosx+cos²x
=1/2sin2x+（1+cos2x）/2
=1/2（sin2x+cos2x）+1/2
=√2/2sin（2x+π/4）+1/2
周期T=2π/ω=2π/2=π
-1≤2sin（2x+π/4）≤1
值域[-√2/2+1/2,√2/2+1/2]