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Trigonometry for College Students ReviewTraditionally located after functions and before calculus, trigonometry combines elementary proofs with everyday applications. Smith follows this mold, but breaks step in a very positive manner. The conventional wisdom has been to consider the trigonometric functions to be the ratios of the sides of a right triangle first, and then generalize. In this case the general functions are followed by the special cases, and it works.
The functions are defined as coordinates on the unit circle and then it is on to the consequences of the definitions. Several obvious identities are immediately presented with proofs, reinforcing the functional approach to trigonometry, as well as introducing the concept of proof. After graphing and additional proofs of identities, the inverse functions are defined. Only then does right angle trigonometry make an appearance. The book closes with complex numbers, polar curves, and conic sections, with much of it being labeled as optional.
As is the case with books of this type, the majority of the problems are standard issue. However, some of them show a great deal of creativity. For example, if you wish to understand the path of Luke Skywalker's fighter as it attacks the Death Star, turn to page 207. And if you need to know how far Mr. T. must throw his grappling hook to catch the top of the building so that he can climb up and stomp the bad guys, turn to page 208. Such problems add spice to the text that will delight all readers with a touch of youth in their hearts.
All chapters end with a list of chapter objectives, key terms, summary problems, and an application for further study. There is an occasional historical note about certain topics and solutions to all odd problems appear at the back of the book. A calculator is required to do the majority of computational style problems.
There are some areas that are poorly done. The inverse trigonometric functions are poorly presented as the restricted graphs of the functions appear after the definitions. It would have been much clearer if the presentation had been more simultaneous. In the preface a technique called framing is introduced, being described as innovative and unique. Actually, it is nothing that the typical teacher of this material will fail to recognize. The taking of one cycle of the function and repeating it after suitable alterations is a standard way of presenting the periodic nature of trigonometry .
However, these weaknesses are in no way fatal, and this book is an excellent option for anyone looking for a textbook of trigonometry with the right mix of functions, proofs, and applications to everyday situations.
There is additional material for this book:
. An answer book for all problems;
. EXPTEST Question bank for IBM compatible computers;
. Instructor's manual;
. Solutions and study guide;
. Trigpak, a computerized tutorial for IBM compatible computers.
Published in Journal of Recreational Mathematics, reprinted with permission.
Trigonometry for College Students OverviewKnown for its student-friendly approach, this book starts with a unit-circle approach. With a focus on applications, it helps students investigate and understand the trigonometric functions, their graphs, their relationships to one another, and ways in which they can be used in a variety of applications.
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