TRIGONOMETRY FOR BEGINNERS BY THE REV. J. B. LOCK, M.A. FELLOW OF GONVILLE AND CAIUS COLLEGE, CAMBRIDGE REVISED AND ENLARGED FOR THE USE OF AMERICAN SCHOOLS BY JOHN A. MILLER, A.M. ASSISTANT PROFESSOR OF MATHEMATICS, LELAND STANFORD JR. UNIVERSITY New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., LTD. 1898 All rights reserved NAAVAL COLLEGE LIBRARY BY EXCHANGE FROM COPYRIGHT, 1896, BY THE MACMILLAN COMPANY. Set up and electrotyped September, 1896. Reprinted February, Norwood Press J. S. Cushing & Co. - Berwick & Smith i PREFACE THE revision of the "Trigonometry for Beginners" differs from that of the original work, chiefly in the following particulars: The subject matter of Chapter VII. formerly followed that of Chapters VIII. and IX.; the addition formulæ are proved for angles of any magnitude, and for more than two angles; a chapter on Inverse Trigonometric Functions and two chapters on Spherical Trigonometry have been added; logarithmic and trigonometric tables have been inserted. The rearrangement has necessitated minor changes in almost every chapter. Throughout the book, the question of ambiguity of solution has received careful attention. It is believed that the clear, simple presentation which characterized the original work has been retained. It has been the endeavor to make definitions that need not be unlearned later; to give proofs, rigorous for the general plane angle; to present as much material as the student will master in a first course; and to present such material as will serve him best in his later studies. The proofs of many propositions are left as exercises for the student. These are formulated, and placed in the body of the text. The lists of examples in the plane trigonometry are, for the most part, those of the original work. Some of the exercises in spherical trigonometry are selected from other texts. Those desiring a shorter course may omit the chapters and the articles marked with an asterisk. I acknowledge my indebtedness to Dr. Frank L. Sevenoak, who kindly permitted the use of his tables, and to friends who aided me by suggestions. JUNE, 1896. JOHN A. MILLER. |