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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010205972 | QA533 G44 2001 | Open Access Book | Book | Searching... |
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Summary
Summary
In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.
Reviews 1
Choice Review
Gelfand (Rutgers Univ.) and Saul (Bronxville Schools, New York) revisit trigonometry, a subject that has been covered by many authors across the last few thousand years. This treatment contains nothing particularly new, but does cover all of the basic topics that a high school or beginning university student should be expected to know: right triangle and unit circle trigonometry. The work is organized informally, perhaps even loosely. There is no index, and the titles of the sections are often cute: the section on Pythagorean triples is titled "Our Best Friends." This may be inviting to some readers, but it certainly makes it difficult to determine what some sections cover when scanning the section titles. There are, on the other hand, 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. Trigonometric identities, inverse trigonometric functions, and graphs of trigonometric and inverse trigonometric functions are also covered. Ninety examples, many exercises, no solutions to exercises, some historical references. Lower-division undergraduates. J. D. Fehribach Worcester Polytechnic Institute
Table of Contents
| Preface |
| 0 Trigonometry |
| 1 What Is New About Trigonometry? |
| 2 Right Triangles |
| 3 The Pythagorean Theorem |
| 4 Our Best Friends (Among Right Triangles) |
| 5 Our Next Best Friends (Among Right Triangles) |
| 6 Some Standard Notation |
| Appendix |
| I Classifying Triangles |
| II Proof of the Pythagorean Theorem |
| 1 Trigonometric Ratios in a Triangle |
| 1 Definition Of Sin [Alpha] |
| 2 Find the Hidden Sine |
