y=sin(x+π/6) (π/6≤x≤2π/3) 值域

问题描述:

y=sin(x+π/6) (π/6≤x≤2π/3) 值域

因为π/6≤x≤2π/3,所以,2π/6≤x+π/6≤5π/6.
当x+π/6=π/2时,即x=π/3,此时y取得最大值,为1;
当x+π/6=5π/6时,即x=2π/3,取得最小值,为1/2;
故y的值域为[1/2,1]