Question

已知函数f(x)=sin(x+π/6),其中x∈【-π/3,a】,若f(x)的值域是【-1/2,1】,则a的取值范围是

Answer 1

由-π/3≤x≤a,

有-π/6≤x+π/6≤a+π/6

设t =x+π/6,如图，由正弦曲线y=sint知,

又y=sint的值域是[-1/2,1],

π/2≤t≤7π/6

即π/2≤a+π/6≤7π/6

解得π/3≤a≤π

所以a的取值范围是[π/3,π]