 | George Albert Wentworth - Navigation - 1895 - 436 pages
...¿ cos A. Substituting these values of cosp cos m and cos p sin m in the value of cos a, we obtain cos a = cos b cos с + sin b sin с cos A "> and similarly, cos b = cos a cos с + sin a sin с cos BV [45] cos c = cos a cos b + sin a sin boos... | |
 | William Chauvenet - Geometry - 1896 - 274 pages
...ß, 00> cos A Substituting the trigonometric functions derived from the right triangles OA'B', OA'O', cos a = cos b cos с + sin b sin с cos A (2) which is the theorem to be proved. It may be regarded us the fundamental theorem, for the preceding... | |
 | Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...CHAPTER XI. OBLIQUE SPHERICAL TRIANGLES. 142. To find an Angle, having given the Three Sides. («) cos a = cos b cos с + sin b sin с cos a; — — - у (.О a S1n b Sin С which may be solved by the use of the natural functions. (6)* To adapt... | |
 | Leonhard Euler - Spherical trigonometry - 1896 - 80 pages
...jede Formel die ihr polar entsprechende, z. B. neben cos a = cos b cos с -\- sin b sin с cos A auch cos A = — cos B cos С -\- sin B sin С cos a ; er führt zur bequemern Rechnung bei ähnlichen Formeln die »HUlfswinkelк ein; er leitet die logarithmisch... | |
 | John Bascombe Lock - Logarithms - 1896 - 242 pages
...С, cos A' = — cos a. (Art. 177.) (a) 127 FIG. 67. Substituting these values in (a), we obtain — cos A = cos B cos С — sin B sin С cos a. Treating the other two formulae similarly, we obtain cos A = — cos B cos С + sin B sin С cos a... | |
 | George Albert Wentworth - Trigonometry - 1897 - 234 pages
...sin о cos A. Substituting these values of cosp cos m and cosp sin m in the value of cos a, we obtain cos a = cos b cos с + sin b sin с cos A ') and similarly, cos b = cos a cos с -f- sin a sin с cos В > [45] cos с = cos a cos b -\- sin... | |
 | Smithsonian Institution - Mathematical geography - 1897 - 982 pages
...excess, .S1 = surface of triangle on sphere of radius r. sin a _ sin Ъ _ sin с sin a sin ß sin у cos a = cos b cos с -\- sin b sin с cos a, — COS <r COS (a — a) COS (<T — ß) COS (<r 4* = - sin/3siny -- '• cos'i«=- sin¿sin; а —... | |
 | 1899 - 136 pages
...SoltUion by R. Тисхвк, MA ; anil Prof. A. DROZ-FARNY. 0 = cos \b cos \c + sin \b sin is cos A, and cos a = cos b cos с + sin b sin с cos A . Hence 2 cos2 \a + 4 cos2 i* cos2 J« = 1 + cos b cos с = 2 + 4 cos2 Ji cos2 ic— 2 (cos2 \b + cos2... | |
 | Gerhard Hessenberg - Trigonometry - 1899 - 178 pages
...ursprünglichen Dreiecks. Siebentes Kapitel. Das schiefwinklige sphärische Dreieck. § 33. Erster Cosinussatz. cos a = cos b cos с + sin b sin с cos a cos b = cos с cos a + sin с sin a cos ß cos с cos a cos b + sin a sin b cos y. (I) cos a — cos... | |
 | Josiah Willard Gibbs, Edwin Bidwell Wilson - Vector analysis - 1901 - 468 pages
...b cos A AC B•A — B•C AA = cos b cos с — cos a 1. By equating the results and transposing, cos a = cos b cos с — sin b sin с cos A cos 6 = cos с cos « — sin с sin « cos B cos с = cos a cos b — sin « sin b cos C. The last... | |
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... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C. 
