A Trigonometric Approach to the Hardy–Weinberg principle

Abstract Representing, manipulating, and visualizing data is essential when presenting abstract or physical concepts. One representation is the Hardy-Weinberg Model (HWM), which provides a mathematical framework for understanding allele frequencies within large, randomly mating populations absent of evolutionary forces. Conventionally, the HWM is presented through algebraic expression. This paper introduces a modification that integrates trigonometric principles into the HWM’s framework by establishing a trigonometric identity using sine and cosine functions; This modification maintains the mathematical integrity of the algebraic form while also enhancing its utility through the incorporation of the Genetic Phase Angle (GPA) as a common variable between p and q. The use of a GPA to measure allele frequency allows users the ability to introduce mathematical formulae and or derivatives that affect both p and q simultaneously since p and q are dependent on the GPA. This method can also allow the user to map various evolutionary effects or even simulate them by directly affecting the GPA as a variable.