 | William Rossiter - 1868 - 186 pages
...(axb) ' = coi Ç «fa * С"~6) 2 si» à (a + 6) (8.) coi a si-» c = cos c cos В + sin В coi A. For, cos a = cos b cos c + sin b sin c cos A ; also, cos 6 = cos c cos a + sin c sin a cos В ; substituting the value of cos b for cos b, in the... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...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... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...b' cos d -f sin V sin d cos A'. But sin a'=s!n A, cos a' = — cos A, sin b' = sin B, &c. Hence — cos A = cos B cos C + sin B sin C cos A ' From this equation we get for cos A' a value equal and with a contrary sign to that which equation... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...article, and recollecting that, cos (180°- A') = - cos A', sin (180°- 7?') = sin B', &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), In... | |
 | Mathematics - 1869 - 124 pages
...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... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...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... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...- 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... | |
 | Johannes Frischauf - Geometry - 1870 - 176 pages
...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 - Comets - 1880 - 662 pages
...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 - 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... | |
| |
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... 
