2kπ-π/2≤x/2+π/3≤2kπ+π/2,即4kπ-5π/3≤x≤4kπ+π/3,k值只能取得0,即函数f（x）=sin(1/2x+π/3),x属于[-2π,2π]的单调递增区间为：【-5π/3,π/3】