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Method of moment analysis of longitudinal radiating slots in the broadwall of a rectangular waveguide requires a careful choice of the basis functions. This is particularly true when we need an accurate evaluation of both longitudinal and transverse components of the Electric field on a slot with finite wall thickness. We show that entire-domain, two-dimensional, sinusoidal basis functions are a successful choice for an accurate and effective modeling of a radiating slot cut in a thick waveguide wall. In this communication we focus on slender slots, which ensure high polarization purity. If a very accurate array design is required, the effect of the longitudinal component of the Electric field, often neglected in the analysis of a narrow longitudinal slot, has shown a significant influence on the slot radiating and circuital properties. The proposed Method of Moment technique has been assessed through comparison with a commercial Finite Element Method software.