a=cos2x+sinx
=1-2*(sinx)^2+sinx t=sinx属于[-1,1]
=1-2t^2+t
t=1/4时,a最大,amax=1-2*1/16+1/4=9/8
t=-1时,a最小,amin=1-2*1-1=-2
所以a属于[-2,9/8]