HYPERBOLIC FUNCTIONS: A GEOMETRIC APPROACH
Preliminary concepts. Hyperbole. Hyperbolic functions. Applications of
hyperbolic functions.
This dissertation has as main objective to present a study on the hyperbolic functions
from a geometric approach in the hyperbola. We will start by reviewing some preliminary
concepts, namely, exponential, logarithmic and trigonometric functions, which
are presented as tools and foundations, so that the denitions and concepts to be studied,
in the course of this work, become more understandable by the reader. Then, we will
define the hyperbola and, in particular, the one with equation xy = a, which will be of
fundamental importance for the definition of hyperbolic functions. With these results, the
hyperbolic sector, the hyperbolic angle and the hyperbolic functions with their characteristics
and properties are defined. Finally, we will present some of the main applications
of hyperbolic functions, in order to consolidate and justify the reason for the development
of this work.