In this paper, we study vertical sectorization techniques in multiple-input single-output (MISO) downlink active antenna systems (AAS). In the AAS, antenna beam patterns can be adjusted in each sector and multiple vertical beams can form the vertical sectorization. Since an exhaustive search based vertical sectorization algorithm requires high computational complexity to find the optimal tilt angles, we propose two vertical sectorization algorithms to reduce the complexity. First, we provide an asymptotic sum rate based algorithm which utilizes a large system approximation of the average sum rate based on the random matrix theory. Next, by using the result in the single sector transmission, the single sector based algorithm is proposed. In the simulation results, we confirm that the proposed algorithms are close to the performance of the exhaustive search algorithm with much reduced complexity.