EXPLORING THE TRIGONOMETRIC CIRCLE AND TRIGONOMETRIC LAWS WITH A GEOGEBRA VISUALIZATION

Shpresa TUDA, Zoran TRIFUNOV

Abstract

Mathematical functions that establish a relationship between the angles of a right triangle and the lengths of its sides are known as trigonometric functions. In this project, we will explore two of the six trigonometric functions and their properties using the trigonometric circle. Initially, trigonometric functions were defined only for acute angles related to right triangles. To extend the sine and cosine functions to functions whose domain is the entire real line, geometric definitions using the unit circle with radius 1 are often used. Then, the domain of the other trigonometric functions is the real line with some isolated points removed. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows the extension of the definition of sine and cosine functions to the entire complex plane and the definition of other trigonometric functions on the complex plane with some isolated points removed. This project discusses the use of GeoGebra in studying trigonometric functions, the Law of Sine, and Law of Cosine. GeoGebra is a powerful mathematical software that allows for the visualization and exploration of trigonometric functions.

Pages: 412 - 418