Do triângulo retângulo ao ciclo trigonométrico: conceitos e aplicações

Abstract

The present work provides an overview of the evolution of trigonometry throughout history, highlighting how some ancient scholars developed and employed the principles we now know as trigonometry. Initially, this theory was essential for determining inaccessible distances and, over time, it began to be applied to the study of periodic movements and the modeling of various natural phenomena. By the 19th century, with the establishment of the so-called Fourier Series, through which we can express various types of functions as a sum of basic trigonometric functions (sine and cosine), trigonometry revealed itself even more as a central and highly relevant subject within both pure and applied mathematics. The present work also proposes an alternative approach to teaching trigonometry in high school. The proposal includes a gradual and logical transition from the study of trigonometry in right-angled triangles to trigonometry on the unit circle. This method aims to provide students with a deeper and more cohesive understanding of the subject, linking historical events with the practical use of this tool over centuries. Through this approach, the goal is not only to facilitate the understanding of trigonometric concepts but also to spark students’ interest in the history and evolution of this important area of mathematics, stimulating their curiosity and engaging them with the subject.