三角函数问题:已知函数f(x)=根号2sin(2x+π/6).x∈[π/12,π/3].求f(x)的值域.

问题描述:

三角函数问题:已知函数f(x)=根号2sin(2x+π/6).x∈[π/12,π/3].求f(x)的值域.

因为x∈[π/12,π/3]
2x∈[π/6,(2π)/3]
(2x+π/6)∈[π/3,(5π)/6]
所以1/2≤sin(2x+π/6)≤1
(根号2)/2≤ 根号2sin(2x+π/6)≤ 根号2
即f(x)的值域为 [(根号2)/2,根号2].