ELEMENTS OF PLANE TRIGONOMETRY WITH FIVE-PLACE TABLES TEXT-BOOK FOR HIGH SCHOOLS, TECHNICAL SCHOOLS AND COLLEGES BY ROBERT E. MORITZ PBJ. NEBRASKA, PH. N. D. STRASSBURG, PROFESSOR OF MATHEMATICS. UNIVERSITY OF WASHINGTON NEW YORK JOHN WILEY SONS, INC. LONDON-CHAPMAN HALL, LIMITED COPYRIGHT, 1910 BY ROBERT . MORITZ Printed in U. S. A. . H. GILSON COMPANY BOSTON. U. S. A. PREFACE TRIGONOMETRY is college mathematics par excellence. To at least 90 per cent of all liberal arts students college mathematics means trigonometry and nothing else. It is important, therefore, that the science be presented in as simple and attractive a manner as possible and that it be made more than a mere method of solving triangles. The first the author tries to accomplish by making the treatment less technical than is customary, by introducing considerable historical matter, by not presupposing a too ready knowledge of elementary mathematics, and none at all of the topics ordinarily treated in college algebra. To accomplish the second point the angle is made the central idea of the science. This permits the enrichment of the science through the introduction of a variety of concepts and processes ordinarily reserved for advanced courses in mathematics. Since the treatment departs considerably from that current in text books on trigonometry, it is fitting that some of the leading characteristics of the present book should be enumerated at the outset First, as to subject-matter 1 The book has been planned to cover five months work at four lessons per week. Each months work is followed by a set of review exercises. Where less time must be given to the subject, certain advanced chapters may, of course, be omitted. 2 The introductory chapter on the graphic method of splving triangles is intended to impress the need of a more accurate method, the method of trigonometry. 3 A knowledge of logarithms has not been presupposed. For this reason a chapter on logarithms and the use of tables has been incorporated at its proper place. Classes who are properly prepared in logarithms may of course omit this chapter. 4 Many of the more important results have been derived by two or more independent methods. This has been done,-- IV PREFACE a To give the teacher a choice of methods. b To offer the ambitious student the advantage which comes from approaching the same truth from two or more directions. c To offer an alternative to the student without a teacher who finds undue difficulty with any one given proof. 5 It is not intended that all the problems should be assigned to any one class. The problems in each set are carefully graded and arranged as follows, a The first half in each set are very simple applications of the principles and theorems discussed in the preceding sections. b The next three or four problems require some originality on the part of the student. c The last few problems in each set are for the more ambitious student and frequently give him the opportunity to dis cover for himself results which are discussed in detail in later sections of the book. 6 Special care has been bestowed on the applied problems illus trating the solution of right and oblique triangles. In each case there is given first a set of problems involving miscellaneous heights and distances. This is followed by separate sets of applied problems from each of the following sciences Physics, Engineering, Navigation, Astronomy and Geography, and Elementary Geometry. These lists arc probably the most varied and complete that have been published in America in recent years. 7 Trigonometric curves have received much fuller treatment than is usual. The method of representing functions by curves is developed from first principles. The treatment includes sine curves of given amplitude and wave length, logarithmic and exponential curves, composition of harmonic curves, the catenary, and the curve of damped vibrations...