y=-2cos^2x+2sinx+3/2
=-2+2sin^2x+2sinx+3/2
=-2+2(sin^2x+sinx+1/4)+1
=2(sinx+1/2)^2-1
当sinx=-1/2即x=-π/6时,y=-1为最小值
当sinx=√2／2即x=π/4时,y=√2+1/2为最大值