 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...more from 90° than another side, is of the same species as its opposite angle. For, by (150), we have cos a = cos b cos с -\- sin b sin с cos A ; whence, . cos a — cos b cos с cos A = - — 5—^- . s1n о sin с in which the denominator is... | |
 | Edward Olney - Trigonometry - 1877 - 220 pages
...plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos о + sin a sin b cos... | |
 | K. E. O. Fritsch, Friedrich Wilhelm Büsing - Architecture - 1879 - 526 pages
...a -j- ß -j- Y — 180° = 2 E (sphärischer Exzess). sin a sin b __ sin с ' sin a sin ß sin f 2) cos a = cos b . cos с + sin b . sin с . cos a 3) cos « = — cos ß . cos Y -\- sin /5 . sin Y • cos e 4) ^ = " ~9Ö°~ 5) cos." = V^1 • sin>-«>... | |
 | Theodor Oppolzer - Comets - 1880 - 664 pages
...A1 + cos A sin с (cos a — cos b cos c) -\- cos A- cos c1 sin b ; beachtet man noch die Relation : cos a — cos b cos с — sin b sin с cos A , so erhellt unmittelbar die eben aufgestellte Hehauptung. Man hat also : sin С da = sin a cos С... | |
 | K. Schmeisser - 1881 - 162 pages
...jtotfc^en jtoei Seiten unb ben ben Seiten gegenüberltegenben SBinïeln gebiíbet toerben. (So ift cos a = cos b . cos с -+- sin b . sin с . cos a, cos a — cos b . cos с cos a = sin b . sin с feos a — cos b . cos c\ 2 , „ , /cos a — cos... | |
 | Briot (M., Charles), Jean-Claude Bouquet - Trigonometry - 1881 - 264 pages
...triangles. Remarques. — On pourrait déterminer directement les éléments с et G par les formules cos a = cos b cos с -(- sin b sin с cos A, cot a sin b = cos b cos G -j- sin G cot A. Si l'on pose tang y = tang ¿> cos A, cot $ = cos b tang... | |
 | Webster Wells - Trigonometry - 1883 - 234 pages
...(180° - A) or (Art. 43) , — cos a = ( — cos 6) cos c, -f- sin ¿> sin с ( — cos A) That is, cos a = cos b cos с + sin b sin с cos A Similarly, we may prove the theorem when b is less than 90°, and с greater than 90°. CASE III. When... | |
 | W. J. C. Miller - Mathematics - 1885 - 242 pages
...II. — If a <JC ^,r, and b, с are each< *т, then cos« is negative, cos b, cose are positive; from cos a = cos b cos с + sin b sin с cos A, cos A is negative, therefore A is obtuse. Similarly, from cos b = cos с cos « + sin e bina cos B... | |
 | De Volson Wood - 1887 - 272 pages
..._ OD OD ' DE DF . cosa-~OE' OF + OE ' OF cos Substituting the trigonometrical functions, group (A), cos a = cos b cos с + sin b sin с cos A \ cos b = cos с cos a + sin с sin a cos .¿? >• (154) cos с = cos a cos b + sin a sin b cos Í7... | |
 | Webster Wells - Trigonometry - 1887 - 200 pages
...coab = cos b tan AD cos AD . , tan AD ., in t. UM\ = sin o = sino cos A (Art. 144). tan b \ > Whence, cos a = cos b cos с + sin b sin с cos A. (37) In like manner we have, cos b = cos с cos a + sin с sin a cos B, (88) and cos с = cos a cos... | |
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... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C. 
