Um estudo da trigonometria numa perspectiva algébrica

Abstract

This work presents a comprehensive examination of trigonometry from an algebraic standpoint, delving into both conventional definitions and efforts to interpret trigonometry through algebraic entities. It covers the fundamentals of conventional trigonometry in the context of right triangles and the trigonometric circle, encompassing topics ranging from trigonometric ratios to trigonometric functions. From this, a quest for a new understanding of trigonometry began.The investigation utilized measurements of the area of a circular sector and keasurements of line segments through the exploration of triangle similarity. Finally, power series were employed for the algebraic construction of cosine and sine in traditional trigonometry. The research has illustrated that adopting an algebraic perspective can enhance the comprehension of trigonometric concepts, establishing connections between traditional elements and innovative approaches. The initial hypothesis, asserting that this algebraic approach could offer novel insights into understanding and applying trigonometry, was validated by demonstrating the possibility of constructing trigonometry through the utilization of algebraic concepts.