 | 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... | |
 | 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... | |
 | 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... | |
 | Aaron Schuyler - Measurement - 1864 - 506 pages
...— B + 180° — C. or — A < 180" — (B + C). . . . A > B + C — 180°. By article 136, we have cos a = cos b cos c -(- sin b sin c cos A. cos a — cos 6 cos c cos .4 = sin b sin r But sin b sin e is positive, since b and c are each less than... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...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 b sin c cos A. (2) cos b — cos a cos c -f- sin o sin c cos B. (3) cos c = cos a cos b + sin a sin b cos (7. 137.... | |
 | 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',... | |
 | 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 have... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 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... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...more from 90° than another side is of the same species as its opposite angle. By article 136, we have cos a = cos b cos c + sin b' sin c cos A. cos a — cos b cos c cos A = sin 6 sin c But sin 6 sin c is positive, since ¿> and c are each less than... | |
 | Karl Klein - Crystallography - 1876 - 456 pages
...cotg A cotg a . sin b = cos b . cos C + sin C . cotg A cotg b . sin a = cos a . cos C + sin C . cotg B cos A = — cos B . cos C + sin B . sin C . cos a ) cos B = — cos C . cos A + sin C . sin A . cos b | cos C = — cos A . cos B + sin A . sin B . cos c ) In folgender... | |
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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. 
