 | Jean-Guillaume Garnier - Geometry - 1812 - 352 pages
...sin. b... (4) J mais , d'après les équations (i)], (2) et (3), on a sin. C sin. e = sin. a cos B cos. a — cos. b cos. c sin. b sin. c cos. b — cos. a cos. c sin. a sin. c cos. c — cos. a cos. b sin. a sin b donc l'équation (4) devient... | |
 | Augustus De Morgan - Spherical trigonometry - 1833 - 40 pages
...b sin. c , or cos. a sin. B sin. C, from <>., have then cos. A + cos. B cos. C = cos. a sin. B sin C, — cos. A = cos. B cos. C — sin. B sin. C cos. «. 'or cos. A write its equal, — cos. (/r — A), and for sin. B its equal, (TT — B), and so on... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...opposite one of the other sides and the angle contained between these two sides. By (a) cos. A= and, cos. C= cos. a — cos. b cos. c sin. b sin. c cos. c — cos. a cos. i sin. a sin. I (1) Hence, cos. c=cos. i+sin. a sin. 6 cos. C. Substituting this... | |
 | William Chauvenet - Trigonometry - 1855 - 264 pages
...applicable to A' BC. Therefore cos a = cos (180° - b) cos (180° - c) + sin (180° - b) sin (180° - c} cos A = (— cos b) (•— cos c) + sin b sin c cos A = cos b cos c + sin 5 sin c cos ul the same result as before. 7. The theorems expressed by (1) and... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...sin n fto° — C) ' which gives cos. a = . and by permuting, cos. I = COS. G = . sin. (180° -) sn. cos. A + cos. B cos. C sin. B sin. C : cos. B + cos. C cos. A sin. C sin. A ' cos. C + cos. A cos. B sin. A sin. B (B.) formula, where the sides... | |
 | Isaac Todhunter - Spherical trigonometry - 1859 - 156 pages
...quadrants. Produce AB and AC to meet in A ; put A'B = c, A'C=V; then from the triangle ABC, as before, C cos a = cos b' cos c + sin b' sin c' cos A'; but b' = ir-b, c'=ir-c, A' = A; thus, (3) Suppose that one of the sides which contain the angle... | |
 | Samuel H. Winter - 1867 - 468 pages
...sin c cos A. Sin A : sin B : sin C : : sin a : sin b : sin c. Cot a sin b = cot A sin C + cos b cos C ; cos A = — cos B cos C + sin B sin C cos a. Sin i A = A / J»in(,-*)sin(,-C)) CQS ^ A = \/ \ sm b sin c } I /sin s sin (sa) \ ;tanJLA_ / ism... | |
 | 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... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...terms of the sides, and the sides in terms of the angles- Thus, from A, From B, (1) CosA = (2) cos в = cos a — cos b cos c sin b sin c ' cos b — cos a cos c sin a sin c ' -- - cose — cosacos b (3) cosC = - - r-—: x sm a sm o A',, . cos... | |
 | Johann August Grunert - Mathematics - 1870 - 586 pages
...^ 0, cos B 4- cos C cos A — sin CVm A ~ 0, cos €4- cos A cos/? — 8\a A sin BNU; und hieraus: cos A + cos B cos C ~ sin B sin C , cos B 4- cos C cos A ^ sin Csin /l , cos f,'4- cos /lcos/f ^ sin/isin B; folglich unter den gemachten Voraussetzungen... | |
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A . sin b = sin a . sin B sin A . sin c — sin a . sin C sin B . sin c = sin b . sin C... 
