 | Silvestre François Lacroix - Geometry, Analytic - 1810 - 556 pages
...par sin b , et ils peuvent ensuite s'écrire ainsi : cos B sin a = cos b sine — cos^sinècosc 1 ._. cos C sin a = sin b cos c — cos A cos b sin c / ' " Si on multiplie la deuxième de ces équations par qu'on l'ajoute à la première , et... | |
 | Robert Woodhouse - Plane trigonometry - 1819 - 300 pages
.../3> ° 5 the spherical angle at 0 ................ C the angle a Ob of the chord ............. 6 then cos. c = sin. a . sin. b . cos. C + cos. a . cos. b (page 139.). But, cos. c = 1 — 2 sin.2 - , and sin. a = 2 sin. ~ cos. | , &c. 2 ^ * .'.1—$. sin.2... | |
 | Charles Bonnycastle - Geometry - 1834 - 670 pages
...equations cos. a = sin. b sin. c cos. A + cos. b cos. c cos. b = sin. asin. c cos. B + cos. a cos. c 39. cos. c = sin. a sin. b cos. C + cos. a cos. b Sect. III. Relations of throe divergent lines. Art. 144. Notation proper to three divergent lines.... | |
 | William Augustus Norton - Astronomy - 1839 - 530 pages
...sides. 74. cos c = cos a cos b -j- sin a sin b cos C cos c = cos (a — 6) — 2 sin a sin b sin3^ C cos C = sin A sin B cos c — cos A cos B sin a cos c = sin c cos a cos B + sin b cos C sin a cot c = cos a cos B + sin B cot C sin a cos B =... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...cos A •= sin B sin C cos a — cos B cos C, 1 cos B = sin A sin C cos b — cos A cos C, *>• (2) cos C = sin A sin B cos c — cos A cos B. \ That is : The cosine of either angle of a spherical triangle, is equal to the product of the sines... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...cos A — sin B sin C cos a — cos B cos C, 1 cos B = sin A sin C cos b — cos A cos C, >• (2) cos C =• sin A sin B cos c — cos A cos B. \ That is : The cosine of either angle of a spherical triangle, is equal to the product of the sines... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...— cos B cos C. (153)In like manner may be deduced cos "Z?=sin C sin A cos b — cos C cos A, (1^4) cos C= sin A sin B cos c — cos A cos B. (155) 151. In any spherical triangle, the cotangent of one side into the sine of another side is equal... | |
 | Franz Brünnow - Spherical astronomy - 1865 - 632 pages
...vice versa: cos A = sin B sin Ccos a — cos B cos C cos B •== sin A sin C cos 6 — cos A cos C (8) cos C = sin A sin B cos c — cos A cos B. 5. If we add the two first of the formulae (3), we find : sin a [sin B + sin C] = sin A [sin b H- sin... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...for any triangle), In the same way, we may deduce, cos B = sin A sin C cos b — cos A cos C • (2.) cos C = sin A sin B cos c — cos A cos .B • (3.) That is, tJ1e cosine of either angle of a spherical triangle is equal to the rectangle of... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...have (1) cos A = sin B sin C cos a — cos B cos C. (2) cos B = sin A sin C cos b — cos A cos C. (3) cos C = sin A sin B cos c — cos A cos B. 138. Proposition IV. The co-sine of one-half of any angle of a spherical triangle is equal to the square... | |
| |
... sin B sin C cos a ; and changing the signs of the terms, we obtain, cos A = sin B sin C cos a — cos B cos C. 
