 | Edward Olney - 1885 - 222 sider
...- A') = 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° — A') = — cos A', etc- ; and sin (180° — B') = sin 3', etcFinally, dropping... | |
 | Johannes Frischauf - 1870 - 178 sider
...Gause'schen u. Neper'schen Gleichungen. 111. . , sin B sin a sin b = : sm A die Seite b, und damit nach cos a = cos b cos c -\- sin b sin c cos A die Seite c. Für die Berechnung setze man q sin Q = cos b q cos Q = sin b cos A, so wird cos a = q... | |
 | Theodor Oppolzer - 1880 - 662 sider
...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... | |
 | Charles Davies - 1872 - 464 sider
...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 - 1872 - 562 sider
...- 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... | |
 | Edward Olney - 1872 - 216 sider
...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... | |
 | 1886 - 418 sider
...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 - 1872 - 472 sider
...- 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... | |
 | Aaron Schuyler - 1873 - 536 sider
...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 - 1873 - 508 sider
...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... | |
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A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a. 
