 | Robert Woodhouse - Plane trigonometry - 1819 - 300 pages
...supplemental triangle ; then, if a, b', c are its sides, A', B', C', its angles, we have, by the form [l], cos. a — cos. b' cos. c cos. A' — sin. b' . sin. c but cos. A' — cos. (180° — a) = — cos. a cos. a = cos. (180° — A)— — cos. A cos. b' =... | |
 | Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...cos a, cos B = — cos A cos C -f- sin A sin C cos 6, cos C = — cos A cos B -f- sin A sin B cos c, cos A -\- cos B cos C cos a = sin B sin C 7 cos B -f- cos ^4 cos C cos £> = ~— f-. — ^ , sm A sin C cos C + cos A cos B cos c = -' . —... | |
 | Miles Bland - Astronomy - 1830 - 394 pages
...C. 50. If A, B, C be three angles, which together make up an odd number of right angles, shew that cos A. cos B. cos C = cos A. sin B. sin C + cos /?. sin A. sin C+ cos C. sin A. sin 5. 51. On the same supposition, shew that cos 2 A + cos 2... | |
 | Classical education - 1831 - 498 pages
...(p cot 9 = cos « tang ß , also cos a = • . ist ; substituirt man diesen Werth in der Gleichung cos a = cos b cos c + cos a sin b sin c, so erhält man nach gehöriger Reduktion sin (c-fiy) cos a sin <p = — -j- — . Endlich bemerken... | |
 | Dr. Gottfried Seebode - 1831 - 572 pages
...dass cot tp cot tp = cos a tang ß, also cos a = r ist; substituirtman diesen Werth in der Gleichung cos a = cos b cos c + cos a sin b sin c, so erhält man nach gehöriger Reduktion sin (c + <p) cos a sin tp = r — . Endlich bemerken wir noch... | |
 | Augustus De Morgan - Spherical trigonometry - 1833 - 40 pages
...developed, will be seen to be cos. a sin. a sin. b sin. c , or cos. a sin. B sin. C, from <>., have then cos. A + cos. B cos. C = cos. a sin. B sin C, — cos. A = cos. B cos. C — sin. B sin. C cos. «. 'or cos. A write its equal, — cos. (/r —... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...cos. A=2 — 2 sec. c sec. 6 cos. a OT, sin-c t cos. c ' cos. b cos. A= cos. A =!_ cos. c ' cos, b cos. a — cos. b cos. c cos. a sin. b sin. c Similarly we shall have, •n COS. & — COS. a COS. C cos. B= — ; cos. C= sin. a sin. c cos. c —... | |
 | Nathan Scholfield - 1845 - 894 pages
...of a side of a spherical triangle in terms of the sines and cosines of the angles. By (/?) we have, cos. A + cos. B cos. C cos- a= sin. B sin. C .'. 1+cos. a= cos. A+cos. B cos. C+sin. B sin. C sin. B sin. C Cos. A+cos. (B—C) sin. B sin. C A+B—... | |
 | Her MAjesty' Inspectors of schools - 1850 - 912 pages
...cos (A -f B) = cos A cos B - sin A sin B. t S. In any plain triangle 4. In any spherical triangle bc cos a = cos b cos c + cos A sin b sin c. Section IV. 1. At what rate is a place iti 45° N. latitude carried per hour by the diurnal revolution... | |
 | Babinet (M., Jacques), Charles Housel - Applied mathematics - 1857 - 424 pages
...laquelle se trouve le triangle. Du reste, il est facile de les rétablir; ainsi, par exemple, la formule cos a — cos b cos c cos A = sin b sin c (*) C'est-à-dire que le rapport de l'angle S avec 9o degrés est égal au rapport de la surface cherchée... | |
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A, 4 cos 6 = cos c cos a + sin c sin a cos B, > (1) . , "cos c = cos a cos b + sin a sin b cos C. J Whence . cos a — cos b... 
