f(x)=cos2x+1/2sinx
=1-2sin2^x+1/2sinx
=-2sin2^x+1/2sinx+1
令t=sinx,t属于[-1,1]
f(x)=-2t^2+1/2t+1
-b/2a=1/8
再根据图像最终得：f(x)=[-3/2,33/32]