| Charles Davies - 1872 - 464 páginas
...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 páginas
...- 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 - 472 páginas
...- 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... | |
| 1886 - 418 páginas
...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 páginas
...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... | |
| Aaron Schuyler - 1873 - 508 páginas
...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 páginas
...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',... | |
| Adrien Marie Legendre - 1874 - 500 páginas
...preceding article, and recollecting that, cos (180°— A') = - cos A', sin (180°- J?') = skl J7', &c, we have, — cos A' = cos B' cos C" — sin B' sin C" cos a' ; or, changing the signs and omitting the primes (since the preceding result is true for any triangle),... | |
| 1882 - 452 páginas
...sin2a and transposing, 1 — cos a cos b cos c = sin* a + sin b sin c cos A cos a; (1) also cosM = — cos A cos B cos C -\- sin B sin C cos a cos A, whence 1 + cos A cos B cos C '= sin1 A + sin B sin Ccos acos A. (2) Dividing (2) by (1), we... | |
| Aaron Schuyler - 1875 - 284 páginas
...b', C=Ш°—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 b'. — cos C' = cos A' cos B' — sin A' sin B' cos... | |
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