%0 Journal Article %T The forgotten p-versine and p-coversine family of functions revisited. %A Alibrahim AH %A Das S %J PLoS One %V 19 %N 8 %D 2024 %M 39137223 %F 3.752 %R 10.1371/journal.pone.0308529 %X This study delves into special class of generalized p-trigonometric functions, examining their connection to the established counterparts like p-cosine and p-sine functions. We here explore the new class of functions called the p-versine, p-coversine, p-haversine, and p-hacovercosine, by providing comprehensive definitions and properties. Grounded in the characteristics of p-cosine and p-sine functions, the newly proposed functions offer unique mathematical insights. Our work contributes towards a thorough understanding of these new special functions, showcasing their potential applications in diverse scientific domains, from mathematical analysis to physics and engineering. This paper contributes as a valuable resource for future applied mathematics researchers, engaging with these new mathematical functions, enhancing the ability to model complex patterns from diverse real-world applications.