令t=sinx,则0＜t≤1
∴y=t/2+2/t
∴y'=1/2-2/t^2
∵0＜t≤1,∴y'＜0
∴y=t/2+2/t在(0,1]上单调减
∴t=1时,即x=π/2时,ymin=5/2