求函数y=cos2x+2sinx-2值域.
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求函数y=cos2x+2sinx-2值域.
![求函数y=cos2x+2sinx-2值域.](/uploads/image/z/15411547-19-7.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0y%3Dcos2x%2B2sinx-2%E5%80%BC%E5%9F%9F%EF%BC%8E)
∵y=cos2x+2sinx-2
=1-sin2x+2sinx-2
=-(sinx-1)2,
∵-1≤sin≤1,
∴-2≤sin-1≤0,
∴(sinx-1)2∈[0,4],-(sinx-1)2∈[-4,0].
∴函数y=cos2x+2sinx-2值域为[-4,0].
=1-sin2x+2sinx-2
=-(sinx-1)2,
∵-1≤sin≤1,
∴-2≤sin-1≤0,
∴(sinx-1)2∈[0,4],-(sinx-1)2∈[-4,0].
∴函数y=cos2x+2sinx-2值域为[-4,0].