Trigonometry / Edition 1

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Trigonometry, a work in the collection of the Gelfand School Program, is the result of a collaboration between two experienced pre-college teachers, one of whom, I.M. Gelfand, is considered to be among our most distinguished living mathematicians. His impact on generations of young people, some now mathematicians of renown, continues to be remarkable. Trigonometry covers all the basics of the subject through beautiful illustrations and examples. The definitions of the trigonometric functions are geometrically motivated. Geometric relationships are rewritten in trigonometric form and extended. The text then makes a transition to the study of algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject. Like other I.M. Gelfand treasures in the program—Algebra, Functions and Graphs, and The Method of Coordinates—Trigonometry is written in an engaging style, and approaches the material in a unique fashion that will motivate students and teachers alike.

From a review of Algebra, I.M. Gelfand and A. Shen, ISBN 0-8176-3677-3:

"The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gel'fand and Shen. There are specific 'practical' problems but there is much more development of the ideas.... [The authors] have shown how to write a serious yet lively book on algebra."

—R. Askey, The American Mathematics Monthly

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Editorial Reviews

From the Publisher

"Cover[s] all of the basic topics that a high school or beginning university student should be expected to know.... There are...some nice touches; for example, a nice informal discussion showing that the sine of an angle in a right triangle does not depend on whether the sides are measured in inches or centimeters..."


"Covers all the basics of the subject through beautiful illustrations and examples…. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject."

— L'enseignement Mathématique

"As a teacher I enjoyed this book enormously and I will doubtless borrow many of the plums to spice up my lessons…. [For] that ideal student who is to be prepared to be challenged to think what the subject is really about, and has the patience to excavate the basic ideas for all they are worth before jumping on to the next chapter, it should prove to be a godsend."

—The Mathematical Gazette

"The authors tried to explain the results of trigonometry as simply as possible…. The exercises include a few problems of each routine type. Most of the problems exhibit a new aspect of the technique or object under discussion. One of the goals of this book is to prepare students for a course in calculus. We recommend it for teachers and students."

—Publicationes Mathematicae

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Product Details

  • ISBN-13: 9780817639143
  • Publisher: Birkhauser Verlag
  • Publication date: 6/8/2001
  • Series: Gel'fand School Outreach Program Series
  • Edition description: 2001
  • Edition number: 1
  • Pages: 229
  • Sales rank: 596,583
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.51 (d)

Table of Contents

0 Trigonometry.- 1 Trigonometric Ratios in a Triangle.- 2 Relations among Trigonometric Ratios.- 3 Relationships in a Triangle.- 4 Angles and Rotations.- 5 Radian Measure.- 6 The Addition Formulas.- 7 Trigonometric Identities.- 8 Graphs of Trigonometric Functions.- 9 Inverse Functions and Trigonometric Equations.

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Customer Reviews

Average Rating 4.5
( 6 )
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Sort by: Showing all of 6 Customer Reviews
  • Anonymous

    Posted August 22, 2005

    The best academic book I have ever touched!

    This book-and any books that are similar to this one-are long overdue and are tremendously needed in classrooms, especially for higher level students. The problem with more of your standard, conventional books that you have at school are that they ONLY tell you how to do something, not why something works like this or that. This is invaluable, for it (the method of solving a problem) then lingers in your brain for a very long time and when you come in contact with some problem not yet the same to it, but somewhat related, you will be able to utilize that knowledge to solve the problem. Whereas by memorizing the steps and 'hows' to do a problem, the person's mind is then very provincial in that area. The person who gave the book two stars above is correct that it is disappointing that there are no solutions, but the overall superb content of the book should put that problem in disguise. Trust me, if you really want to LEARN, buy and read carefully through this book!!!! It will be very beneficial.

    2 out of 2 people found this review helpful.

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  • Anonymous

    Posted September 24, 2004

    A fascinating examination of trigonometry.

    This clearly written text, which is designed as a supplement to a trigonometry course, is a fascinating study of the subject. After reviewing the geometric prerequisites, the authors cover right triangle trigonometry, the relationship between trigonometry and geometry, unit circle trigonometry, trigonometric identities, graphs of trigonometric functions, and inverse trigonometric functions. The book touches on subjects not normally covered in trigonometry courses. Particularly noteworthy are appendices to the later chapters in which the authors relate trigonometry to Pythagorean triples, use sequences of trigonometric functions to approximate pi, and introduce Fourier series. There are numerous worked examples to give the reader insights that will help her or him solve the many difficult problems in the text. Solutions to the problems are not provided.

    2 out of 2 people found this review helpful.

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  • Posted January 28, 2009


    I haven't dealt with Trigonometry (or Algebra/Geometry) for over 10 years and now I need it for my work. I found this book on here (sadly it was not easy to find... I found it because I sorted by lowest price).<BR/><BR/>I take it B&N wants you to buy the expensive books rather than the ones that are truly amazing when they are less expensive.<BR/><BR/>Instantly while reading this book I was refreshed with not only the trigonometry I needed but also the geometry and algebra that back it up. It was concise, clear as glass, this author really understands how the human mind learns.<BR/><BR/>I didn't come away feeling as though I'd memorized formulas; each time I closed the book I felt enriched with a greater understanding of math.<BR/><BR/>This book is suitable for brand new students and is better than the textbooks I received in school; but also suitable for review after a long time such as is my case. It's not bloated and it speaks well with it's illustrations. It's very suited for visual learners like myself.<BR/><BR/>There are no solutions to the problems; I found that I did not require any. This book offers true education.<BR/><BR/>Why is this not at schools? And for it's price? It's sad something like this is hidden away, really. Get this in the schools!!

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  • Anonymous

    Posted November 15, 2002

    Dont bother with this one

    The book covers all topis however there are no solutions to the problems. What good is a book without solutions! Dont waste your money

    0 out of 1 people found this review helpful.

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  • Anonymous

    Posted August 14, 2009

    No text was provided for this review.

  • Anonymous

    Posted October 31, 2008

    No text was provided for this review.

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