PREFACE. IN revising his Plane and Spherical Trigonometry, the author has effected many important improvements. The attention of teachers is specially invited to the following features of the new work: 1. The proofs of the functions of 0°, 90°, 180°, and 270°; §§ 22 to 25. 2. The proofs of the functions of 120°, 135°, etc.; § 27. 3. The method of finding the values of the remaining functions of an angle when the value of any one is given; § 28. 4. The proofs of the functions of (-A), and (90° + A), in terms of those of A; §§ 29, 30. 5. The method of solution in the examples of §§ 34 and 35. 6. The general demonstration of the formulæ for sin (x + y) and cos (x + y); § 42. 7. The discussion of the line values of the functions, and their application in tracing the changes in the six principal functions of an angle as the angle increases from 0° to 360°; §§ 60, 61. 8. The discussion of trigonometric equations in § 62. 9. The solution of right triangles by Natural Functions; see Ex. 1, page 54. 10. The discussion of the ambiguous case in the solution of oblique triangles; §§ 117 to 120. 11. The proof of the formulæ for the values of x in the cubic equation ―ax-b=0; § 126. 12. The geometrical proof of the important theorems of § 133. 13. The demonstration of the formulæ for right spherical triangles before those for oblique spherical triangles; see Chapters XI. and XII. 14. The reduction of the number of cases in the complete demonstration of the fundamental theorems for spherical right triangles, to three, by application of the theorems of § 133; see § 136. iii 15. The solution of Quadrantal and Isosceles Spherical triangles; §§ 149, 150. 16. The discussion of the ambiguous cases in the solution of oblique spherical triangles; §§ 165, 166; especially the rules given on pages 108 and 111 for determining the number of solutions. At the end of Chapter XII. will be found a collection of formulæ in form for convenient reference. The revised work contains a much greater number of examples than the old; they have been selected with great care, and are with few exceptions new. The results have been worked out by aid of the author's new Six Place Logarithmic Tables, which contain also a Table of Natural Functions, and an Auxiliary Table for Small Angles. The Trigonometry can be obtained either with or without the Tables. MASSACHUSETTS INSTITUTE OF TECHNOLOGY, 1896. WEBSTER WELLS.. |