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
"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 Mathematique
"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."