 | Franz Brünnow - Astronomy - 1851 - 634 pages
...B. die drei Formeln zu berechnen: cos a = cos b cos c + sin b sin c cos A sin n sin B = sin b sin A sin a cos B = cos b sin c — sin b cos c cos A so setze man: sin b cos A = m sin M cos b — m cos M Dann wird: cos a = m cos (c — M) sin a sin... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...sin. b cos. a cos. C. If we apply the principle of the Polar Triangle to equations (I) they become t sin.- A cos. b = cos. B sin. C + sin. B cos. C cos. a ; I sin. A cos. c = cos. C sin. B + sin. C cos. B cos. a. sin. B cos. c = cos. C sin. A + sin. C cos.... | |
 | Franz Brünnow - 1865 - 584 pages
...for every spherical triangle : cos a = cos b cos c -+- sin b sin c cos A sin a sin 5 = sin b sin, A sin a cos B = cos b sin c — sin b cos c cos A. These are the three principal formulae of spherical trigonometry and express but a simple transformation... | |
 | Franz Brünnow - Spherical astronomy - 1865 - 632 pages
...true for every spherical triangle: cos a = cos b cos c + sin b sin c cos A sin a sin B = sin b sin A sin a cos B = cos b sin c —• sin b cos c cos A. These are the three principal formulae of spherical trigonometry and express but a simple transformation... | |
 | Johannes Frischauf - Geometry - 1870 - 176 pages
...cos A, woraus sin b cos A — cos a sin c — sin a cos c cos B oder durch entsprechende Vertauschung sin a cos B = cos b sin c — sin b cos c cos A \ sin a cos C = cos c sin b — sin c cos b cos AJ entsteht, und ebenso für die beiden übrigen Seiten... | |
 | Johannes Frischauf - Geometry - 1877 - 216 pages
...cos A , woraus sin b cos A = cos « sin c — sin a cos c cos B oder durch entsprechende Vertauschung sin a cos B — cos b sin c — sin b cos c cos A \ ,„^ sin a cos С «•• cos c sin b — sin c cos b cos A } entsteht, und ebenso für die beiden... | |
 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...from which we may determine a, B, and 6', when b, c, and A are given : sin a sin B = sin b sin A ; sin a cos B = cos b sin c — sin b cos c cos A ; sin a sin C = sin c sin A ; (6) sin a cos (7 = sin b cos c — cos b sin c cos A. cos a = cos 5 cos... | |
 | Wolf, Charles Joseph Étienne Wolf - Astronomy - 1891 - 434 pages
...— sin a' cot b' -\- cos C' cosa' ou, en rétablissant lés éléments du triangle considéré : (5) sin A cos b = cos B sin C + sin B cos C cos a (6) cos A = — cos B cos C + sin B sin C cos a (7) sin C cot B = sin a cote — cos C cos a Ces formules... | |
 | William Wallace Campbell - Spherical astronomy - 1891 - 190 pages
...[Chauvenef's Sph. Trig. § 114] the general equations cos a — cos b cos c + sin b sin c cos A, (1) sin a cos B = cos b sin c —sin b cos c cos A, (2) sin a sin B = sin b sin A. (3) To adapt these equations to the triangle POZ, let A = PZO =180°... | |
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A sin a cos B = cos b sin c —• sin b cos c cos A. 
