Essentials of Trigonometry with Applications [antikvár]

PREFACEThe distinguishing features of this book are (1) a concise presentation of the fundamental part of plane trigonometry up to the solution of triangles; (2) the use of five-place logarithms in the solution of triangles and in other applications, with due allowance for the accuracy of data; (3) a chapter on spherical trigonometry; (4) a chapter on applications, which has been written to give essential preparation to those who may enter upon military or naval service. ''J'his text, therefore, should not only meet the needs of students for whom trigonometry is mainly useful as an introduction to further courses in mathematics, but it should be especially valuable for those who are interested in applications.The first five chapters are taken from the authors' text A Brief Course in Trigonometry with minor revision. In the next three cliapters part of the material has been adapted from the same text and from the authors' Trigonometry, Plane and Spherical. Most of the last chapter is new.Use of Coordinates. As in their other texts, the authors have here made use of coordinates, almost from the start. In preparatory courses in mai,hematics, students have become familiar with rectangular coordinates. The briefest and best introduction to trigonometry, we believe, is based on the utihzation of this knowledge, together with the use of polar coordinates. This makes it relatively simple to start with the general angle and to give proofs that apply to all cases. It also lays a firm foundation for the study of analytic geometry and calculus.Applications. Throughout the first eight chapters both text and (íx(írcis(!s i)rcsent many applications of trigonometry to problems of cnfiincieriiig and of other sciences. The ninth chapter is devoted to the use of ti-igoiiometry in sm'veying, in problems connected with maps and with ai-tillery, and in navigation. Under the last head will be foiuid se(!t,ions on plane sailL^ig,; parallel sailing, dead reckoning, gr(iat cii'iile sailing, and celestial mavigation. In connection with the use of ai'tiliery such terms as the mil arc explained, and problems of aiming are briefly treated.