y=sin(x+π/6)（π/6≤x≤2π/3）值域

Question

y=sin(x+π/6)　（π/6≤x≤2π/3）　值域

Answer 1

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]