An Introduction to Trigonometry and its Applications


by

Vasile Postolică

DOI: 10.2174/97816080595081140101
eISBN: 978-1-60805-950-8, 2014
ISBN: 978-1-60805-951-5



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An Introduction to Trigonometry and its Applications presents a systematic approach to explain trigonometry concepts and applications. The tex...[view complete introduction]

Table of Contents

Foreword

- Pp. i-ii (2)

Solomon Marcus

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Preface

- Pp. iii-iv (2)

Vasile Postolică

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Sets. Relations. R and R¯

- Pp. 1-28 (28)

Vasile Postolică

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Real Functions of Real Arguments

- Pp. 29-48 (20)

Vasile Postolică

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Vectors in R3

- Pp. 49-59 (11)

Vasile Postolică

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The Fundamental Trigonometric Functions and the Customary Inversive Restrictions

- Pp. 60-83 (24)

Vasile Postolică

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Applications

- Pp. 84-125 (42)

Vasile Postolică

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References

- Pp. 126

Vasile Postolică

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Subject Index

- Pp. 127-129 (3)

Vasile Postolică

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Foreword

To many generations trigonometry was one of the mathematical subjects taught in school, along with arithmetic, algebra, geometry, and analysis. For some time now, due to the need to diminish the syllabus, trigonometry stops being considered a distinct subject with its own handbook, and is included in the syllabus for algebra, geometry and analysis. Under these circumstances, the unitary nature of trigonometry is sacrificed. But there are still enough pupils interested in mathematics, enough graduates and students, not to mention the math teachers, the numerous engineers and economists that are still fond of elementary, school mathematics, but who would like to reconsider it from a superior point of view, that is from the perspective of mathematic knowledge accumulated in time. This book, written rigorously, but passionately, has a perspective that is equally based on the ensemblist structure of modern mathematics, on the elements of real analysis and the axiomatic fundaments of geometry, and it reaches climax with the applications that imply analytic algebraic and geometric abilities. From the historical presentation of mathematics given in the book the reader can, for example, learn the surprising fact that, from a chronologically point of view, plane trigonometry was preceded by spherical trigonometry, necessary in astronomy, although the latter is more complex than the former. The author of this book, Professor Vasile Postolică, teaching at “Vasile Alecsandri” University of Bacău, is a mathematician that has convincingly asserted himself in research, with results published in exacting publications, results that have become a part of the international circuit. His vast experience in school and university teaching made possible the development of this successful experiment, experienced by few professors: the re-writing of a chapter of school mathematics from a superior point of view. This adventurous path has been taken by mathematicians like Felix Klein and Jacques Hadamard, hence this is a very serious project. We congratulate Professor Vasile Postolică for this success. At the same time, supposing that he will continue this adventure, we suggest that he broaden the perspective by introducing elements of trigonometric series and Fourier series, that are, probably, the most important use of the trigonometric functions, having a particular relevance in physics. Some elements of spherical trigonometry would be also timely. The present book deserves to be successful in book stores and justifies every one of our praises to its author.

Academician Solomon Marcus,
Piatra NeamN,
România


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.

CONFLICT OF INTEREST
None Declare

ACKNOWLEDGEMENT
None Declare

Vasile Postolică,
Romanian Academy of Scientists,
“Vasile Alecsandri” University of Bacău,
România,
Email: vpostolica@ambra.ro

List of Contributors

Author(s):
Vasile Postolică
University of Cambridge
Kings College
Cambridge
UK




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