 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...cos. 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.... | |
 | Jean Marie C. Duhamel - 1868 - 966 pages
...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... | |
 | William Rossiter - 1868 - 186 pages
...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 +... | |
 | Royal Astronomical Society - Astronomy - 1871 - 718 pages
...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)... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...= — cos B cos c + sin B sin c cosa ; ) (2) cos B = — cos A cos c + sin A sin C cos b ; \ B. (3) cos C = — cos A cos B + sin A sin B cos c. ) GENERAL FORMULA. we have a = 180° - A', ft = 180° — B', c = 180° - C', A = 180* - a', B = 180°... | |
 | Astronomy - 1872 - 412 pages
...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... | |
 | Benjamin Williamson - Calculus - 1873 - 406 pages
...connecting the Variations of Three Sides and One Angle. — Differentiating the well-known relation cos c = cos a cos b + sin a sin b cos C, regarding a and b as constants, we get dc sin a sin b sin C dC sin c = sin a sin B. dc Again, the value... | |
 | Aaron Schuyler - Navigation - 1873 - 536 pages
...group, (1) cos a = cos b cos c -f- sin b sin c cos A. (2) cos b = cos a cos c + sin a sin c cos J3. (3) cos c = cos a cos b + sin a sin b cos C. 137. Proposition III. The co-sine of either angle of a spherical triangle is equal to the product of... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...cos A'— cos B' cos C" — sin B' sin C" cos a'. — cos B' = cos A' cos 0" — sin A' sin C' cos b'. — cos C" = cos A' cos B' — sin A' sin B' cos d. Changing the signs and omitting the accents, since the formulas are true for any triangle, we have... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...cos A'—~ cos B' cos C' — sin B' sin C" cos a'. — cos. B'= cos A' cos C"— sin A' sin C' cos b'. — cos C' = cos A' cos B' — sin A' sin B' cos c'. Changing the signs and omitting the accents, since the formulas are true for any triangle, we have... | |
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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. 
