Contents
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Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill Education eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com. Dr. ROBERT E.
MOYER taught mathematics and mathematics education at Southwest Minnesota State University in Marshall, Minnesota from 2002 to 2009 and served as an adjunct professor of mathematics there from 2009 to 2012. Before coming to SMSU, he taught mathematics and mathematics education at Fort Valley State University in Fort Valley, Georgia from 1985 to 2000. He served as head of the Department of Mathematics and Physics from 1992 to 1994. Prior to teaching at the university level, Dr. Moyer served at the K-12 mathematics consultant for seven years at Middle Georgia Regional Educational Service Agency, a five-county education cooperative in central Georgia. Dr.
Moyer taught high school mathematics for seven years in Rantoul, Illinois and for five years in Carmi, Illinois. He has developed and taught numerous inservice courses for mathematics teachers. He received his Doctor of Philosophy in Mathematics Education from the University of Illinois (Urbana-Champaign) in 1974. He received his Master of Science in 1967 and his Bachelor of Science in 1964, both in Mathematics Education from Southern Illinois University (Carbondale). The late FRANK AYRES, JR., PhD, was formerly professor and head of the Department at Dickinson College, Carlisle, Pennsylvania. He is the author of eight Schaums Outlines, including Calculus, Differential Equations, 1st Year College Math, and Matrices.
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Preface
In revising the fifth edition, the strengths of the earlier editions were retained. There will still be the 20 online videos demonstrating the solution of some of the supplementary problems in the text.
It is still possible to solve all the problems without the use of a calculator by using the tables provided, by using a basic scientific calculator, or by using a graphing calculator. The text is flexible enough to be used as a primary text for trigonometry, a supplement to a standard trigonometry text, or as a reference or review text for an individual student. The book is complete in itself and can be used quite well by students studying trigonometry for the first time and by students needing to review the fundamental concepts and procedures of trigonometry. It is a helpful source finding a specific piece of trigonometric information needed in another course or on a job. Each chapter contains a summary of the necessary definitions and theorems for a particular aspect of trigonometry followed by a set of solved problems. These solved problems include the proofs of theorems and the derivation of formulas.
Each chapter ends with a set of supplementary problems with their answers. Triangle solution problems, trigonometric identities, and trigonometric equations require a knowledge of elementary algebra and basic geometry. The problems have been carefully selected and their solutions spelled out in sufficient detail and arranged to illustrate clearly the algebraic processes involved as well as the use of the basic trigonometric relations. ROBERT E. MOYER
Contents
Angles and Applications
1.1 Introduction
Trigonometry is the branch of mathematics concerned with the measurement of the parts, sides, and angles of a triangle.
Plane trigonometry, which is the topic of this book, is restricted to triangles lying in a plane.
Trigonometry is based on certain ratios, called trigonometric functions, to be defined in the next chapter. The early applications of the trigonometric functions were to surveying, navigation, and engineering. These functions also play an important role in the study of all sorts of vibratory phenomenasound, light, electricity, etc. As a consequence, a considerable portion of the subject matter is concerned with a study of the properties of and relations among the trigonometric functions.