Plane And Spherical Trigonometry - Softcover

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Many American text-books on trigonometry treat the solution of triangles quite fully jE nglish text-books elaborate analytical trigonometry; but no book available seems to meet both needs adequately. To do that is the first aim of the present work, in the preparation of which nearly everything has been worked out and tested by the authors in their classes. The work entered upon, other features demanded attention. For some unaccountable reason nearly all books, in proving the formulae for functions of a p, treat the same line as both positive and negative, thus vitiating the proof; and proofs given for acute angles are (without further discussion) supposed to apply to all angles, or it is suggested that the student can draw other figures and show that the formulae hold in all cases. As a matter of fact the average student cannot show anything of the kind; and if he could, the proof would still apply only to combinations of conditions the same as those in the figures actually drawn. These difficulties are avoided by so wording the proofs that the language applies to figures involving any angles, and to avoid drawing the indefinite number of figures necessary fully to establish the formulae geometrically, the general case is proved algebraically (see page 58). Inverse functions are introduced early, and used constantly. Wherever computations are introduced they are made by means of logarithms. The average student, using logarithms for a short time and only at the end of the subject, straightway forgets what manner of things they are. It is hoped, by dint of much ju-ctice, extended over as long a time as possible, to give the student a command of logarithms that will stay. The fundamental formulae of trigonometry must be memorized. There is no substitute for this. For this purpose oral work is introduced, and there are frequent lists of review problems involving
(Typographical errors above are due to OCR software and don't occur in the book.)