 | 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... | |
 | 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... | |
 | 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 —... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | James Morford Taylor - Trigonometry - 1905 - 256 pages
...A . (5) Substituting in (3) for cos AD cosp and sin AD cosp their values in (4) and (5), we obtain cos a = cos b cos с + sin b sin с cos A. [42] Similarly, or by symmetry from [42], we have cos b = cos с cos a + sin с sin a cos B, cos e... | |
 | Friedrich Gauss - 1906 - 394 pages
...о. 2. Das schiefwinklige sphärische Dreieck. JITJ U (49) sin a sin a tin b sin ß sin с sin (50) cos a = cos b cos с + sin b sin с cos a. (51) cos Ь = caí a cos с 4- sin a sin с cos ß. ( 5Z ) cos с = cos a cos b + sin a sin b cos y.... | |
 | William Carpenter Pendleton Muir - Nautical astronomy - 1906 - 754 pages
...azimuth to find the variation in / di to a variation in h. Taking the fundamental trigonometric formula cos a = cos b cos с + sin b sin с cos A, ein A sin b = sin B sin a, and substituting A = Z, B = M, a = 90° — d, b = 90° — с = 90 —... | |
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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. 
