COPYRIGHT, 1913, BY THE MACMILLAN COMPANY. Set up and electrotyped. Published May, 1913. Reprinted Norwood Press J. S. Cushing Co. - Berwick & Smith Co. PREFACE IN Trigonometry, as elsewhere, a motive for the study of each topic is necessary to secure the effective attention of the student. The knowledge required for the actual solution of triangles - the one motive common to all texts on Trigonometry - is only a fraction of the traditional course, even when the refinements necessary for logarithmic solution are included. Thus, the addition formulas, as such, the solution of trigonometric equations, and all reference to angles larger than 180°, are unnecessary for any process of solution of plane triangles. In order to share with the student the teacher's knowledge that these other topics are of real importance, other practical problems of an elementary nature are used to introduce them. Thus, composition and resolution of forces is made an introduction to the study of large angles, and is used to illustrate the meaning of the addition formulas. Large angles are also used in problems on rotation and angular speed. Radian measure is shown to be useful in problems on rotation and on mensuration. Topics for which no wide application exists that is within the student's present grasp - such as De Moivre's theorem and infinite series are omitted. Thus the book contains a minimum of purely theoretical matter. Its entire organization is intended to give a clear view of the meaning and the immediate usefulness of Trigonometry. The proofs, however, are in a form that will not require essential revision in the courses that follow. As The solution of triangles remains the principal motive. such, it is attacked immediately and no diversion is indulged in until this problem has been completely solved. A sharp distinction is made between the fundamental principles of solu V tion of triangles and those other processes that deal with speed and accuracy. The arrangement is such that the student makes steady progress in his ability to perform operations and to solve problems that actually occur in practice. The geometric methods of solution of triangles occupies the first five pages; the principles of trigonometric solution of right triangles are completed in the next ten pages; accurate solution of right triangles, the principles of solution of oblique triangles, the detailed logarithmic methods, follow in uninterrupted succession. Thus the student may stop at almost any point with a complete grasp of definite processes whose value is clear to him, to which all that he has studied has contributed. The number of exercises is very large, and the traditional monotony is broken by illustrations from a variety of topics. Here, as well as in the text, the attempt is often made to lead the student to think for himself by giving suggestions rather than completed solutions or demonstrations. The text proper is short; what is there gained in space is used to make the tables very complete and usable. Attention is called particularly to the complete and handily arranged table of squares, square roots, cubes, etc.; by its use the Pythagorean theorem and the Cosine Law become practicable for actual computation. The use of the slide rule and of fourplace tables is encouraged for problems that do not demand extreme accuracy. Only a few fundamental definitions and relations in Trigonometry need be memorized; these are here emphasized. The great body of principles and processes depends upon these fundamentals; these are presented in this book, as they should be retained, rather by emphasizing and dwelling upon that dependence. Otherwise, the subject can have no real educational value, nor indeed any permanent practical value. A. M. KENYON, L. INGOLD, E. R. HEDRICK, EDITOR. § 15. Applications of Projections 17. Products with Negative Factors Exercises VIII. Right Triangles. Miscellaneous Exercises. 23 § 34. Directed Lines and Segments. Vectors § 35. Geometric Addition of Line Segments. § 36. Subtraction of Line Segments § 37. Rotation. Directed Angles. § 38. Geometric Addition and Subtraction of Directed Angles 52 § 27. The Tangents of the Half-Angles § 28. Second Proof of the Law of Tangents Exercises XII. Logarithmic Solution of Case II Exercises XIII. Logarithmic Solution of Case III § 31. Logarithmic Solution of Case IV. The Ambiguous Case 40 PART IV APPLICATIONS 40 |