Associate Professor of Mathematics, Armour Institute of Technology, AND CHARLES WILBUR LEIGH Associate Professor of Mathematics, Armour Institute of Technology FIRST EDITION MCGRAW-HILL BOOK COMPANY, INC. 6 BOUVERIE STREET, LONDON, E. C. COPYRIGHT, 1914, BY THE Stanhope Press F. H. GILSON COMPANY BOSTON, U.S. A. PREFACE THIS text has been written, because the authors felt the need of a treatment of trigonometry that duly emphasized those parts necessary to a proper understanding of the courses taken in schools of technology. Yet it is hoped that teachers of mathematics in classical colleges and universities as well will find it suited to their needs. It is useless to claim any great originality in treatment or in the selection of subject matter. No attempt has been made to be novel only; but the best ideas and treatment have been used, no matter how often they have appeared in other works on trigonometry. The following points are to be especially noted: (1) The measurement of angles is considered at the beginning. (2) The trigonometric functions are defined at once for any angle, then specialized for the acute angle; not first defined for acute angles, then for obtuse angles, and then for general angles. To do this, use is made of Cartesian coördinates, which are now almost universally taught in elementary algebra. (3) The treatment of triangles comes in its natural and logical order and is not forced to the first pages of the book. (4) Considerable use is made of the line representation of the trigonometric functions. This makes the proof of certain theorems easier of comprehension and lends itself to many useful applications. (5) Trigonometric equations are introduced early and used often. (6) Anti-trigonometric functions are used throughout the work, not placed in a short chapter at the close. They are used in the solutions of equations and triangles. Much stress is laid upon the principal values of anti-trigonometric functions as used later in the more advanced subjects of mathematics. (7) A limited use is made of the so-called "laboratory method" to impress upon the student certain fundamental ideas. (8) Numerous carefully graded practical problems are given and an abundance of drill exercises. |