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We study a novel “coverage by directional sensors” problem with tunable orientations on a set of discrete targets. We propose a Maximum Coverage with Minimum Sensors (MCMS) problem in which coverage in terms of the number of targets to be covered is maximized whereas the number of sensors to be activated is minimized. We present its exact Integer Linear Programming (ILP) formulation and it is used as a baseline for comparison. Then we provide a distributed greedy algorithm (DGA) solution. By incorporating a measure of the sensors’ residual energy into DGA, we further develop a Sensing Neighborhood Cooperative Sleeping (SNCS) protocol which performs adaptive scheduling on a larger time scale. Finally, we evaluate the properties of the proposed solutions and protocol in terms of providing coverage and maximizing network lifetime through extensive simulations.