y=sin²x+acosx-1/2a-3/2
=1-cos²x+acosx-1/2a-3/2
=-cos²x+acosx-1/2a-1/2
=-cos²x+acosx-a²/4+a²/4-1/2a-1/2
=-(cos²x-acosx+a²/4)+a²/4-1/2a-1/2
=-(cosx-a/2)²+a²/4-1/2a-1/2
当cosx-a/2=0时,函数y的值最大
-1