A key challenge in developing energy-efficient sensor networks is to extend network lifetime in resource-limited environments. As sensors are often densely distributed, they can be scheduled on alternative duty cycles to conserve energy while satisfying the system requirements. Directional sensor networks composed of a large number of directional sensors equipped with a limited battery and with a limited angle of sensing have recently attracted attention. Many types of directional sensors can rotate to face a given direction. Maximizing network lifetime while covering all of the targets in a given area and forwarding sensor data to the sink is a challenge in developing such rotatable directional sensor networks. In this paper, we address the maximum directional cover tree (MDCT) problem of organizing directional sensors into a group of non-disjoint subsets to extend network lifetime. One subset, in which the directional sensors cover all of the targets and forward the data to the sink, is activated at a time, while the others sleep to conserve energy. For the MDCT problem, we first present an energy-consumption model that mainly takes into account the energy expenditure for sensor rotation as well as for the sensing and relaying of data. We also develop a heuristic scheduling algorithm called directional coverage and connectivity (DCC)-greedy to solve the MDCT problem. To verify and evaluate the algorithm, we conduct extensive simulations and show that it extends network lifetime to a reasonable degree.