-π/6<=x<=π/2
-π/3<=2x<=π
sin在(-π/2,π/2)递增,(π/2,3π/2)递减
所以2x=π/2时最大=sinπ/2=1
最小在边界
sin(-π/3)=-√3/2,sinπ=0
所以值域[-√3/2,1]