Preface

Trigonometry appeared as a part of medieval geometry, at first the spherical component required by astronomy, after that plane trigonometry was developed. In 1260 the most extensive work in this field was created “ The Treatise of the Complete Quadrilateral”, written by Näsr-ad-Din, followed by the first synthesis of trigonometric knowledge of the 15th century elaborated by Regiomontanus. By studying and developing applied mathematics, the Indians have introduced the sine function as association of any circle arc having half the length of the under tightened cord by the arc’s double, the term “sine” and some interpolator methods of calculating the values of this function were given by Peuerbach, and the natural connections between algebra, mathematical analysis and trigonometry appeared in the 18th century. Using the major elements of the Basis of Mathematics, the book briefly, but rigorously presents in the first chapter sets, relations, and the algebraic-topologic structure for R and R , properties of real functions of real argument in the second chapter, and the concept of vector in R3, described in the third chapter. The book presents itself as an original and synthetic approach that allows a quick learning of the fundamental trigonometric functions and the corresponding inversive restrictions thoroughly analyzed in the fourth chapter, followed by the suggestive applications in the last chapter, without any further consultation of some additional bibliography. The theoretical considerations and the applicative issues are significant proving to be very useful for everyday classes, different exams and the methodic-scientific improvement. Thus, the book addresses anyone who is interested not only in properly knowing trigonometry, but also in the major elements regarding one of the essence of mathematics. It is the result of the unrests of a teenager fascinated by mathematics and of the responsibilities of the teacher he has come to be and it is also of interest to: advanced high school students, undergraduates, and mathematics teachers. The author shows great responsiveness towards any suggestion meant to improve the contents and the presentation, with thanks everyone who has made possible the publishing of this book.