显然当(x/2+π/6)∈[-π/2+2kπ,π/2+2kπ]（k为整数）时,sin(x/2+π/6)单调递增,→(x/2)∈[-π/2-π/6+2kπ,π/2-π/6+2kπ]=[-2π/3+2kπ,π/3+2kπ],→x∈[-4π/3+4kπ,2π/3+4kπ]（k为整数）.