 | 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 - 428 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 - 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... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...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... | |
 | 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',... | |
 | Aaron Schuyler - Measurement - 1873 - 520 pages
...— 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 0" — sin A' sin C' cos b'. — cos C" = cos A' cos B' — sin A' sin B' cos... | |
 | Adrien Marie Legendre - Geometry - 1874 - 512 pages
...= sin b sin c cos A ; (2.) and now substituting these values of OE, OL, and QP, in ( 1 ), we have, cos a = cos b cos c + sin b sin c cos A • (3.) la the same way, we may deduce, cos b = cos a cos c + sin a sin c cos B • • (4.) cos c... | |
 | Electronic journals - 1882 - 452 pages
...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 - Measurement - 1875 - 276 pages
...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... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 202 pages
...cos AD sin c cos b sin AD . • . cos a = I . cOS AD cOS AD and from [3] tan AD = cos A tan b ; . . . cos a = cos b cos c + sin b sin c cos A, and similarly cos b = cos c cos a + sin c sin a cos B, cos c = cos a cos b + sin a sin 6 cos C. NOTE.... | |
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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... 
