Quality-of-service in terms of network connectivity and sensing coverage is important in wireless sensor networks. Particularly in sensor scheduling, it must be controlled to meet the required quality. In this paper, we present novel methods of the connected coverage optimization for sensor scheduling using a virtual hexagon partition composed of hexagonal cells. We first investigate the optimum number of active sensors to fully cover an individual hexagonal cell. According to the best case, a sensor selection method called the three-symmetrical area method (3-Sym) is then proposed. Furthermore, we optimize the coverage efficiency by reducing the overlapping coverage degree incurred from the 3-Sym method, which is called the symmetrical area optimization method. This considers coverage redundancy within the particular area, namely, sensor's territory. The simulation results show that we achieve not only complete connected coverage over the entire monitored area with the near-ideal number of active sensors but also the minimum overlapping coverage degree in each scheduling round