 | Eli Todd Tappan - 1868 - 432 pągines
...cos. (180°— A) = cos. (180° — B) cos. (180° — C) + Reducing (829), and changing the signs, cos. A = — cos. B cos. C + 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... | |
 | Benjamin Greenleaf - 1869 - 516 pągines
...Applying (150) to A'BC1, we have cos a' = cos If cos ci -\- sin V sin c1 cos A' ; or, by (46), — cos A = cos B cos C — sin B sin C cos a ; whence, cos A = sin B sin C cos a — cos B cos i7. (153) In like manner may be deduced cos B= sin... | |
 | 1869 - 124 pągines
...pt = tan Ci tan c2 = tan b tan c cos A tan p2 = sin o, tan B, = tan p cot B cot C sec a, sin b sin c cos A cos B cos C sin B sin C cos a cos b cos c ' therefore, at once, tan3 k = — which, substituting for the functions of the angles... | |
 | Johannes Frischauf - 1870 - 176 pągines
...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 pągines
...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... | |
 | Edward Olney - 1885 - 222 pągines
...- 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... | |
 | Edward Olney - 1872 - 472 pągines
...- 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... | |
 | Charles Davies - 1872 - 464 pągines
...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... | |
 | 1886 - 418 pągines
...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 - 216 pągines
...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... | |
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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... 
