Excerpt from Plane Trigonometry
This book is designed to meet the needs of beginners who wish to master the fundamental principles of Trigonometry. The authors aim has been to prepare a text-book which shall be clear and practical, yet thoroughly scientific.
The proofs of formulas are simple but rigorous. The use of directed lines is consistent; the directions of such lines in the figures are usually indicated by arrowheads, and these lines are always read from origin to end. Both trigonometric ratios and trigonometric lines are employed, but at first the ratios are used exclusively until they have become fixed in mind and familiar. It is proved that the ratios are the measures of the lines, and that, therefore, any relation which holds true for the one holds true for the other also.
The distinction between identities and equations is emphasized in definition, treatment, and notation. The solution of trigonometric equations is scientific and general. The trigonometric ratios are defined in pairs as reciprocals of each other both to aid the memory and to emphasize one of the most important of their fundamental relations. In the reduction of the functions of any angle to those of an acute angle, the theorems concerning the functions of -A and 90 +A are made fundamental. The addition formulas are proved for positive or negative angles of any quadrant and from them are deduced the other formulas concerning the functions of two or more angles. When two or more figures are used in a proof, the same phraseology always applies to each figure.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. Это и многое другое вы найдете в книге Plane Trigonometry (Classic Reprint) (James M. Taylor)