 | Elmer Adelbert Lyman, Edwin Charles Goddard - 1900 - 228 pàgines
...= — cos B cos C + sin B sin C cos a, Similarly, cos B = — cos A cos C + sin A sin C cos b, and cos C = - cos A cos B + sin A sin B cos c. 97. In any spherical triangle to prove gHLJ:=gHLg=sm C. sin a sin b sin a c • . cos a — cos 6 cos... | |
 | Robert Stawell Ball - 1900 - 584 pàgines
...sin a sin b sin c ' 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. Thus the formulae of spherical trigonometry are generally applicable throughout the extent*. * I learned... | |
 | Josiah Willard Gibbs, Edwin Bidwell Wilson - 1901 - 470 pàgines
...results and transposing, 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. The last two may be obtained by cyclic permutation of the letters or from the identities (BxC).(AxB)... | |
 | George Albert Wentworth - 1903 - 346 pàgines
...C = sin c sin A. {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 C. f cos A — — cos B cos C + sin B sin C cos a. 46. -I. cos B = — cos ^4 cos C + sin ^. sin C cos... | |
 | University of Sheffield - 1905 - 574 pàgines
...method to prove the fundamental theorems of the theory of poles and polars 10. — Prove the formula cos c = cos a cos b + sin a sin b cos C The opposite sides of an equi-lateral spherical quadrilateral whose side is a are perpendicular to... | |
 | Preston Albert Lambert - 1905 - 120 pàgines
...formulas, cos a = cos Ъ cos c -f sin b sin c cos A, (19) cos b = cos a cos c + sin a sin c cos B, cos c = cos a cos b + sin a sin b cos C, express relations between the six parts of a triedral angle. Hence if any three parts are given the... | |
 | Simon Newcomb - 1906 - 580 pàgines
...included angle C. r• • sin c sin A = sin a sin C, sin c cos A = cos a sin b ~ sin a cos b cos C, -. cos c = cos a cos b + sin a sin b cos C. If we compute k and K from k sin K=s\na cos 0, kcosK=cosa, then sin c cos A = k sin (b - K), cos c... | |
 | Daniel Alexander Murray - 1906 - 466 pàgines
...sin c cos A. (2) Similarly, or by taking the sides in turn, cos b = cos c cos a + sm c SMI a cos B, cos c = cos a cos b + sin a sin b cos C. In words : In a spherical triangle the cosine of any side is equal to the product of the cosines of... | |
 | Joseph Claudel - 1906 - 758 pàgines
...quantities a + b and a — b substituted in (1) or (2) give C. C may also be calculated directly. Thus, cos C = — cos A cos B + sin A sin B cos c, or cos C = — cos A (cos 5 — sin B tan B cos c). Let tan B cos c = cot 9, then cos C = — cos A... | |
 | Sir George Howard Darwin - 1908 - 540 pàgines
...sin b + cos a cos b cos C = sin a sin b + cos c cos C — sin a sin b cos2 C = sin a sin b sin* C + cos c (— cos A cos B + sin A sin B cos c) = sin A sin B sin' c + sin A sin B cos2 c — cos A cos B cos c = sin i sinj — cos i cosj cos N Substituting... | |
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B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G. 
