 | Theodor Oppolzer - Comets - 1880 - 662 pages
...A2 + cos A sin c (cos a — cos b cos e) -+- cos A1 cos c2 sin b ; beachtet man noch die Relation: cos a — cos b cos c = sin b sin c cos A , so erhellt unmittelbar die eben aufgestellte Behauptung. Man hat also: sin C da = sin a cos C d B... | |
 | Adrien Marie Legendre - Geometry - 1871 - 490 pages
...that, cos (180°— .4') = - cos A', sin (180°— B') = sin -B', <fcc., we have, — cos A' = cos J5' cos C" — sin -B' sin C' cos a' ; or, changing the...(since the preceding result is true for any triangle), cos A = sin B sin C cos a — cos B cos C ( 1.) In the same way, we may deduce, cos B = sin A sin C... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...substituting this value La (2), we have, (20 and now substituting these values of OE, OZ>, and QP, in (1), we h'ave, cos a — 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... | |
 | Edward Olney - Trigonometry - 1872 - 216 pages
...cos (180° - B') cos (180° - C') . , + sin (180° - B.') sin (180° — C') cos (180° - a"), or, cos A' = — cos B' cos C' + sin B' sin C' cos a", since cos (180° — АО = — cos A', etc. ; and sin (180° — a') = sin a'. Finally, dropping the... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...- AО = cos (180° - B') cos (180° - CO + sin (180° - B') sin (180° — CO cos (180° - «0. or, cos A' = — cos B' cos C' + sin B' sin C' cos a', since cos (180° — AО = — cos A', etc. ; and sin (180° — BO = sin B', etc. Finally, dropping... | |
 | Mathematics - 1886 - 418 pages
...of this relationship may be shown thus : — Any parts between 0 and TT which satisfy the equation cos a = cos b cos c •+• sin b sin c cos A can form a spherical triangle, because cos(S~c), cosa and cos (b + c) would be in descending order... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...- AO = cos (180° - B1) cos (180° - C7) + sin (180° - B') sin (180° — C') cos (180" - a'), or, cos A' = — cos B' cos C' + sin B' sin C' cos a', since cos (180° — A*) = — cos A', etc. ; and sin (180° — B1) = sin B', etc. Finally, dropping... | |
 | Aaron Schuyler - Navigation - 1873 - 536 pages
...6', C=180° — c'. Substituting these values in the formulas of the preceding article and reducing, we have, — cos A'= cos B' cos C" — sin B' sin C" cos a'. — cos B'= cos A' cos C" — sin A' sin C" cos 6'. — cos C"=cos A' cos B' — sin A' sin B' cos... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...cos EOF= cos b cos c. NM= EM sin MEN = sin b cos A sin c. Substituting the values of OD, OF, and NM, we have cos a = cos b cos c + sin b sin c cos ^4. In like manner other, formulas may be deduced, giving the group, (1) cos a = cos b cos c + sin... | |
 | Harvard University - 1873 - 732 pages
...Obtain the first two formulas used in the previous question, by means of the following equations: — cos a = cos b cos c + sin b sin c cos A, k sin <(> = sin ft cos A, k cos # = cos 6. 7. Given in a spherical oblique triangle, B = 22° 48',... | |
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A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B... 
