sin(x-π/6)-1≥0,
sin(x-π/6)≥1,
∴sin(x-π/6)=1,
x-π/6=π/2+2kπ,k∈Z;
∴x=2π/3+2kπ,k∈Z;
∴定义域为﹛x|x=2π/3+2kπ,k∈Z;﹜