作业帮求函数f(x)=2sin²x+2sinx-1/2,x∈[π/6,5π/6]的值域
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![求函数f(x)=2sin²x+2sinx-1/2,x∈[π/6,5π/6]的值域](/uploads/image/z/1077828-60-8.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%3D2sin%26%23178%3Bx%2B2sinx-1%2F2%2Cx%E2%88%88%5B%CF%80%2F6%2C5%CF%80%2F6%5D%E7%9A%84%E5%80%BC%E5%9F%9F)
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求函数f(x)=2sin²x+2sinx-1/2,x∈[π/6,5π/6]的值域
求函数f(x)=2sin²x+2sinx-1/2,x∈[π/6,5π/6]的值域
求函数f(x)=2sin²x+2sinx-1/2,x∈[π/6,5π/6]的值域
(x)=2sin^2x+2sinx-1/2=2(sinx+1/2)^2-1
x属于[π/6,5π/6]
所以1/2≤sinx≤1
与是1≤f(x)≤7/2
即值域为[1,7/2]