y=4cosx+3sin^2x+2
=4cosx+3(1-cos^2x)+2
=-3cos^2x+4cosx+5
=-3(cos^2x-4cosx/3+4/9)+5+4/3
=-3(cosx-2/3)^2+19/3
当cosx=2/3时有最大值19/3
当cosx=-1时有最小值-2