 | Benjamin Greenleaf - 1862 - 518 pàgines
...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... | |
 | Isaac Todhunter - 1863 - 182 pàgines
...free from ambiguity. Or we may determine C without previously determining a and b from the formula cos C = — cos A cos B + sin A sin B cos c. This formula may be adapted to logarithms, thus; cos C = cos B (— cos A + sin A tan B cos c) ; assume... | |
 | Saturnino Montojo - 1865 - 302 pàgines
...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 - 1866 - 762 pàgines
...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... | |
 | Jean Marie C. Duhamel - 1868 - 966 pàgines
...équations suivantes : ' cosa =cosicosc -f- sine sine cos A, cos b = cos « cos c + sin a sin c cos B, cos c — cos a cos b -+- sin a sin b cos C. On les démontre d'abord dans le cas où l'angle est plus petit que deux droits, et les côtés qui le... | |
 | William Rossiter - 1868 - 186 pàgines
...are repeated here for convenience of reference. ,-, ч sin A _ sin В _ sin С sin a sin b sin c (2.) cos c = cos a cos b + sin a sin b cos C. (3.) cot a sin c = cos c cos В + s ¿re В cot A. (4.) <(i»±+I=«*С «*(?=»> 2 2 ras J (»t +... | |
 | Eli Todd Tappan - 1868 - 444 pàgines
...B cos. C -f- sin. B sin. C cos. a. Similarly, cos. B = — cos. A cos. C -j- sin. A sin. C cos. b, cos. C = — cos. A cos. B + sin. A sin. B cos. c. None of the above formulas is suited for logarithmic calculation. FORMULA8 FOR LOGARITHMIC U8B. SSO.... | |
 | Royal Astronomical Society - 1871 - 718 pàgines
...the geometrical proof would be more simple, I give the analytical one, as it may be useful. We have cos C = — cos A cos B + sin A sin B cos c, and thence — sinC<fC = (sin A cos B + cos A tin B co» e) d A + (sin B cos A + tin A cos B cos c)... | |
 | Charles Davies - 1872 - 464 pàgines
...— cos b cos c + sin b sin c cos A • (3.) Jj the same way, we may deduce, cos b = cos a cos c + sin a sin c cos B • ' (4.) • cos c = cos a cos b + sin a sin 6 cos (7 • • (5.) That is, the cosine of either side of a spherical triangle is equal to the rectangle... | |
 | 1872 - 412 pàgines
...the geometrical proof would be more simple, I give the analytical one, as it may be useful. We have cos C = — cos A cos B + sin A sin B cos c, 208 Prof. Cayley, on the Orbit xxxil. 5, and thence — tin C •." C = (sin A cos B + cos A sin B... | |
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B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G. 
