 | P. L. Cirodde - 1847 - 114 pàgines
...smc= — : — ; — . smA De sina sin£ cosC = cosc — cosacos^, nous tirerons cosc = sin a sin b cos C -\- cos a cos b , et , en substituant ces valeurs...de cos c dans sin b sin c cos A = cos a — cos b cosc, nous trouverons sin a sin b sin C cos A . , , ,, ,, - : — 7 - = cosa — sm a sm o coso cosC... | |
 | 1859 - 698 pàgines
...für eine aufser z auch x und x' gemessen hat. Winkel WMN durch A, so hat man: cos a — cos b cos c + sin b sin c cos A cos a' — cos b cos c — sin b sin c cos A oder Bezeichnet man den Bogen MN durch b und den (3) , l a'-Hfl «' — i COS... | |
 | Isaac Todhunter - 1859 - 156 pàgines
...opposite angle of one triangle, and a' and A' similar quantities for the other. Then cos a = cos b cos c + sin b sin c cos A, cos a'= cos b cos c + sin 6 sin c cos A! ; therefore cos a - cos a = sin 6 sin c (cos A — cos A") ; that is, sin ^ (a... | |
 | Isaac Todhunter - 1863 - 182 pàgines
...opposite angle of one triangle, arid a and A' similar quantities for the other. Then cos a = cos b cos c + sin b sin c cos A, cos a' = cos b cos c + sin b sin c cos A'; therefore cos a - cos a' = sin b sin c (cos A — cos A') ; that is, sin ^ (a... | |
 | Lefébure de Fourcy (M., Louis Etienne) - 1868 - 350 pàgines
...the opposite parts; and formula (11), Art. 157, and formula (1), Art. 149, cos A = — cos B cos C + sin B sin C cos a cos a = cos b cos c + sin b sin c cos A, become, since A = 90°, and therefore cos A = 0 and sin A = 1, oosa = cotB cotC,or,... | |
 | Aaron Schuyler - 1875 - 284 pàgines
...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 180°. If a diners... | |
 | Webster Wells - 1887 - 200 pàgines
...halfangles of a spherical triangle in terms of the sides of the triangle. From (87), Art. 156, we obtain sin b sin c cos A = cos a — cos b cos c, , cos a — cos b cos c ,_ . or, cos-4 = - .• (B) s1n o sm c Subtracting both members from unity,... | |
 | 1894 - 258 pàgines
...formule dus sinAB C—rinb.sinc.sinA^tinc. sina.sinB = sina. sinb. sin C. Hieruit volgt vooreerst (wegens sin b . sin c . cos A = cos a — — cos b . cos c) dat sin2 ABC = (l — cos2 6) (l — cos2 c) — — (cos a — cos 6 . cos c)2 = l — cos2 a —... | |
 | 1896 - 414 pàgines
...cotg C = 4R* sin A sin B cos C, Ph = 4R2 cos A cos B cos C ; par conséquent P0 + Pt + Pc - Ph = 4R! (sin B sin C cos A + ••• — cos A cos B cos C) = - 4R2 cos (A + B + C) = 4 Rl, ME LKMOINE déduit très simplement les relations de M. Droz Farny... | |
| |
That is, cos a' = cos b' cos c' + sin 6' sin c' cos A'. .: cos (180° - A) = cos (180° - B) cos (180° - C) + sin (180° - B) sin (180° - '7' cos (180° - a). [Art. 16. d.] .: — cos A = (— cos B) (— cos C) + sin B sin C(— cos a). 
