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PLANE TRIGONOMETRY

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FOR

COLLEGES AND SECONDARY SCHOOLS

BY

DANIEL A. MURRAY, B.A., Ph.D.

INSTRUCTOR IN MATHEMATICS IN CORNELL UNIVERSITY
FORMERLY SCHOLAR AND FELLOW AT JOHNS HOPKINS UNIVERSITY

LONGMANS, GREEN, AND CO.

91 AND 93 FIFTH AVENUE, NEW YORK

LONDON AND BOMBAY

Educt 168.99.585


hiervard University,
Dopt. of Education Library

to
HARVARD LULLLUE LIBRARY

Año 1o 1921

COPYRIGHT, 1899,
By LONGMANS, GREEN, AND CO.

ALL RIGHTS RESERVED.

Norwood Press
J. S. Cushing & Co. - Berwick & Smith

Norwood Mass. U.S.A.

PREFACE.

ALTHOUGH there are already many excellent text-books on trigonometry, there appears still to be room for one which shall avoid the extremes of expansion and brevity. Some of the most thorough and scholarly of these contain a great variety of matters which it is impossible to consider in the time usually assigned to this study in school and college. On the other hand, the explanations given in many other works are so meagre that the student is perplexed and bewildered by the new ideas which are so abruptly forced upon him, and the difficulties of the teacher are greatly increased. The manner of presentation adopted in this volume necessitates more reading matter, and, consequently, a somewhat larger number of pages than is found in many of the recent text-books on trigonometry. This has seemed unavoidable, however, for the general consensus of opinion among those with whom the author has conferred, is that it is essential to explain in some detail the principles of the science, in order that it may be clearly and intelligently understood by an elementary student.

With regard to the scope of the book, it may be said that it deals with the subjects considered in the ordinary course in plane trigonometry in colleges and secondary schools. It discusses the topics usually required for teachers' certificates, for entrance to college, and for examinations in trigonometry in the first year of the college curriculum. It treats of all the topics that one who has taken a few months' course in trigonometry may be reasonably expected to know.

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