函数y=2-sinx-cos²x(x∈R)的值域是A.[3/4,+∞)B.(3/4,+∞)C.[3/4,1]D.[3/4,3]
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![函数y=2-sinx-cos²x(x∈R)的值域是A.[3/4,+∞)B.(3/4,+∞)C.[3/4,1]D.[3/4,3]](/uploads/image/z/3857648-32-8.jpg?t=%E5%87%BD%E6%95%B0y%3D2-sinx-cos%26%23178%3Bx%EF%BC%88x%E2%88%88R%EF%BC%89%E7%9A%84%E5%80%BC%E5%9F%9F%E6%98%AFA.%5B3%2F4%2C%2B%E2%88%9E%EF%BC%89B.%EF%BC%883%2F4%2C%2B%E2%88%9E%EF%BC%89C.%5B3%2F4%2C1%5DD.%5B3%2F4%2C3%5D)
函数y=2-sinx-cos²x(x∈R)的值域是A.[3/4,+∞)B.(3/4,+∞)C.[3/4,1]D.[3/4,3]
函数y=2-sinx-cos²x(x∈R)的值域是
A.[3/4,+∞)
B.(3/4,+∞)
C.[3/4,1]
D.[3/4,3]
函数y=2-sinx-cos²x(x∈R)的值域是A.[3/4,+∞)B.(3/4,+∞)C.[3/4,1]D.[3/4,3]
y=2-sinx-cos²x
=2-sinx-1+sin²x
=sin²x-sinx+1
=(sinx-1/2)²+3/4
最小 3/4
最大 9/4+3/4=3
所以选 D.[3/4,3]
D