 | John Daniel Runkle - Mathematics - 1861 - 436 pages
...— C) =. cos(?r — A) COS(TT — B) -\- sin (TT — A) X sin(?r — B) COS(TT — c), that is, — cos C = cos A cos B — sin A sin B cos C ; and now, if the spherical triangle ABC be rightrangled at C, that is, if C= 90°, these two equations... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...B, O A' 0, we have cos a = cos b cos c -f- sin b sin c cos A. In like manner may be deduced cos 6 = cos c cos a -(- sin c sin a cos B, cos c = cos a cos 6 -f- sin a sin 6 cos C. The preceding construction supposes the sides b and c, which contain the angle... | |
 | William Thomas Read - 1862 - 144 pages
...triangle, and the included angle, to find the third side. Let a, b, and angle C be given. Kg. 21. Since cos c = cos a cos b + sin a sin b . cos C, and cos C = (2 cos2 -^ — 1); therefore, Q cos c = cos a cos b + sin a sin b . (2 cos2 -~ 1) 0 = cos... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...cosine of the included angle. By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b -\- sin a sin b cos C; and by means of (147), sin C sin c = sin a --. — -.. sin A . , „. , . sin a sin b cos A sin C cosa... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...triangles 0 A' O A' O, we have cos a = cos b cos c -)- sin b sin c cos A. In like manner may be deduced cos b = cos c cos a -)- sin c sin a cos B, cos c = cos a cos b -)- sin a sin J cos C. (1^2) BOOK V. 150. In any spherical triangle, the cosine of any angle is eqi1/tl to tlie product... | |
 | Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...C) + sin (IT— B) sin (IT —C) cos (TT- a), that is, cos A = — cos B cos C + sin B sin C cos a. Similarly cos B = — cos C cos A + sin C sin A cos b, and cos C = — cos -4 cos 5 + sin A sin -B cos c. 48. The formulae in Art. 44 will of course remain... | |
 | Saturnino Montojo - 1865 - 302 pages
...ya deducir por la permutacion indicada (39) las siguientes cos a = cos b cos c + sin b sin c cos A \ cos b = cos c cos a + sin c sin a cos B > («, „) cos c = cos a cos b + sin a sin b cos C ,• en las cuales como se hallen relacionados entre sí t<w dos los elementos del triángulo en toda... | |
 | Albrecht Schrauf - Crystallography - 1866 - 762 pages
...cotg v» 2. Bekannt ab G sin c sin B = sin ft sin C sin c cos J? = sin a cos b — cos a sin b cos (7 cos c = cos a cos b -\- sin a sin b cos C cotg a sin ft — cos b cos C „ cotg b sin a — cos a cos C B = - ! - ; - f= -- sin G ÜUS /2 -A... | |
 | William Chauvenet - Trigonometry - 1924 - 268 pages
...sin O = sin c sin BL (3) sin c sin A = sin a sin (7 cos a = cos 6 cos c .+ sin 6 sin c cos J. cos 6 = cos c cos a + sin c sin a cos B cos c = cos a cos 6 + sin a sin b cos (7 8. Let A'B'O', Fig. 5, be the polar triangle of ABO, and designate its angles... | |
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A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b... 
