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Connectivity is a crucial requirement for wireless sensor network deployments. Without being able to guarantee a reasonable level of connectivity, many critical network operations may not be possible. Traditionally, omni-directional antennas have been used for communication in wireless sensor networks. In this paper, we analyze the effects on connectivity when a hybrid approach towards antennas is employed, by using both omni and sectorized uni-directional antennas. We present results that help understand the relationship between node density, transmission radius, uni-directional antenna beam width and network connectivity. We demonstrate that, under a broad class of conditions, a hybrid sectorized approach drastically improves connectivity and reaches higher probabilities of 100% connectivity at much smaller node densities and transmission radii. We also suggest neighborhood management procedures for a hybrid approach and comment on the costs involved in practically implementing our paradigm.