y=cos²x-sinx求值域
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y=cos²x-sinx
=-sin²x-sinx+1
=-(sin²x+sinx+1/4)+5/4
= -(sinx+1/2)²+5/4
∵-1<=sinx<=1
∴-1/2<=sinx+1/2<=3/2
∴0<=(sinx+1/2)²<=9/4
-9/4<=-(sinx+1/2)²<=0
∴-1<= -(sinx+1/2)²+5/4<=5/4
∴值域是[-1，5/4}
=-sin²x-sinx+1
=-(sin²x+sinx+1/4)+5/4
= -(sinx+1/2)²+5/4
∵-1<=sinx<=1
∴-1/2<=sinx+1/2<=3/2
∴0<=(sinx+1/2)²<=9/4
-9/4<=-(sinx+1/2)²<=0
∴-1<= -(sinx+1/2)²+5/4<=5/4
∴值域是[-1，5/4}
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