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

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]