An Introduction to Trigonometry and its Applications

In this chapter we will briefly present the fundamental terminology of mathematics regarding notions such as set and, respectively, relation, mentioning the algebraic-topological structures for R and R^__ sets.

This chapter contains a significant sequence of the properties for the real functions of real arguments, also important for the introduction of the fundamental trigonometric functions. Here are included only the properties considered appropriate for defining and describing the essential trigonometric functions. the range of these representative qualities is larger and it is also suggested by the selective bibliography mentioned further on.

In the beginning we will present the first complete axiomatic system for Euclidean geometry elaborated in 1899 by David Hilbert as a sinthesis of Lectures on the Foundations of Geometry, 1891-1902.

This part of this book is devoted to the fundamental trigonometric functions examined together with their inverted restrictions, following the main directions of studies specified at the end of Chapter 2.

This section is for the essential algebraic connections related to the trigonometric functions introduced in the precedent chapters and for the immediate implications and applications in the Euclidean geometry.