Tensor satisfying binary law for the equation including the trigonometric function

Description

This article investigates how tensor analysis can incorporate trigonometric functions within the framework of a Binary Law. It begins by establishing a fundamental tensor equation that satisfies specific conditions under this law, where a trigonometric function, represented as Aμ=sin⁡(xν)A^\mu = \sin(x^\nu)Aμ=sin(xν), emerges from exploring the equation’s properties. However, the application of other trigonometric functions within this tensor framework under Binary Law remains unexamined. The article expands the discussion by introducing superposition scenarios for a function in the form of Mμ=Msin⁡(xν)M^\mu = M \sin(x^\nu)Mμ=Msin(xν). It explores two main superposition cases: one between different functions with unique positions and another between identical functions with varying phases. Finally, it delves into how these superpositions relate to the concept of force, offering a fresh perspective on tensor applications involving trigonometric functions under Binary Law.