Evolution and Significance of Sine Function in Ancient Indian Mathematics

This research article delves into the historical and mathematical intricacies of the construction of sine functions, particularly focusing on ancient Indian mathematical concepts and their evolution. It begins by highlighting the significance of sine (jya) as a fundamental trigonometric function in Indian mathematics, alongside its synonyms in Sanskrit. The historical journey of the term “sine” is traced back to ancient Indian mathematical texts, which were later translated into Arabic and then into Latin, ultimately leading to the adoption of the term “sine” in modern mathematics. The article elaborates on the definitions and interpretations of sine (ज्या), cosine (कोटिज्या), versed sine (उत्क्रमज्या), and co-versed sine (कोट्युत्क्रमज्या) in Indian mathematical traditions. It explains how these functions were conceptualized and utilized in astronomical calculations, emphasizing their geometric and trigonometric significance. Furthermore, the article discusses the division of a circle into quadrants (Vṛttapādas) and the concept of Trijyā (radius), highlighting the mathematical sophistication and terminology used by ancient Indian mathematicians. Several mathematical formulas related to the construction and calculation of sine functions are presented, including formulas for finding sine values at specific angles such as 45 degrees, 18 degrees and 72 degrees. These formulas showcase the mathematical ingenuity and problem-solving skills of ancient Indian mathematicians. Overall, this research article provides a comprehensive overview of the historical development and mathematical foundations of sine functions in ancient Indian mathematics, shedding light on their enduring legacy and contributions to modern trigonometry.