y=cos²x+sinx
=1-sin²x+sinx
=-(sin²x-sinx)+1
=-(sinx-1/2)²+5/4
令t=sinx
y=-(t-1/2)²+5/4
此为二次函数,开口向下,因为-1≤t≤1
当t=-1的时候,y有最小值y=-1