Question

函数y=2sin(x+π/6) x∈【 -π/2,π/2】的值域是(要过程）

Answer 1

解由x∈【 -π/2,π/2】

得-π/2≤x≤π/2

即-π/3≤x+π/6≤2π/3

故当x+π/6=π/2时,sin(x+π/6)=1,此时y=2sin(x+π/6)有最大值2

当x+π/6=-π/3时,sin(x+π/6)=-√3/2,此时y=2sin(x+π/6)有最小值-√3.

故函数的值域为[-√3,2].