Uma construção alternativa da trigonometria hiperbólica

Abstract

In books on Differential and Integral Calculus one comes acrosshyperbolic trigonometry in such a way that first the hyperbolic sine and cosine are defined using two mathematical formulas, and only later it is shown that a branch of the hyperbola can be parameterized by the hyperbolic sine and cosine. Furthermore, there is another construction of     hyperbolic trigonometry, presented by McMahon (1906), relating the area of a sector of the ellipse centered at the origin with the area of a sector of
the equilateral hyperbola. The objective of this paper is to present a construction of hyperbolic trigonometry based on the graph of a hyperbola and also using the concept of area and logarithm, and only then carry out an
investigation in search of the mathematical formulas that define them. In general, hyperbolic trigonometry and real hyperbolic trigonometric functions were studied using only the concept of limit and its properties and also analytical geometry.