 | Lefébure de Fourcy (M., Louis Etienne) - Geometry, Analytic - 1859 - 578 pages
...Étant donnés les trois côtés a, b, c, trouver les angles A, B, C. L'équation [1] du n" 96 donne cos a — cos b cos c cos A = : — — : sin b sin c mais comme le calcul logarithmique ne s'applique point à cette expression, on se sert des formules... | |
 | Isaac Todhunter - Spherical trigonometry - 1859 - 156 pages
...formula will be a relation in Plane Trigonometry. For example, in Art. 106, from the formula we deduce , cos a — cos b cos c cos A = - : — = — -. sin b sin c now suppose r to become infinite ; then ultimately and this is the expression for the cosine of the... | |
 | 1859 - 682 pages
...angle from its logarithmic sine, or the converse. X. Prove that XHI. Prove that in a spherical triangle cos a — cos b cos c cos A = sin b sin c a, b, c, being the sides, and A the angle opposite the side a. Adapt the expression for cos A to logarithmic... | |
 | John Daniel Runkle - Mathematics - 1861 - 436 pages
...fundamental formula of spherical trigonometry, cos a = cos b cos c -j- sin b sin c cos A ; . • . cos a cos A = cos b cos c cos A -(- sin b sin c cos2 A ; and as this formula is of course also true for the polar triangle, whose sides and angles... | |
 | William Thomas Read - 1862 - 144 pages
...sm C cos B = 0, sin B = 1 ; therefore, cos a = c.os „. sin C (3) or, cos A = cos a sin C . Again, cos a — cos b . cos c Cos A = sin b . sin c cos b but cos a = therefore cos A = cos c cos b — cos b . cos2 c sin b sin c cos c _ cos b (1 —... | |
 | Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...cos a cos b cos c), and this is equal to cos a sin B sin C sin2 a sin b sin c, (Art. 41) ; therefore cos A + cos B cos C = cos a sin B sin C. Similarly the other two corresponding formulae may be proved. Thus the formulae in Art. 47 are established;... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...to express sin^a, cos^a, tangía, in functions of the angles A, B, C. We deduce from formula (11), cos A + cos B cos C cos a = sin B sin C. By operations analogous to those in Art. 153, we readily deduce the formulae required. Placing A +... | |
 | Elias Loomis - Spherical astronomy - 1868 - 522 pages
...accented, d', Z', and h'. Also, let TT represent the parallax in declination. By Trig., Art. 225, we have cos. a— cos. b cos. c cos. A= : — ; — : . sin. b sin. c This formula, applied successively to the triangles APZ and BPZ, gives cos. AP - cos. PZ cos. AZ cos.... | |
 | Johannes Frischauf - Geometry - 1870 - 176 pages
...Dreieckes, dessen Seiten im Vorhältnisse zum Halbmesser der Kugel sehr klein sind. 1. Setzt man in , cos a — cos b cos c COS A = — . — : — sin b sin c für Sinus und Cosinus der Seiten die Reihen , und vernachlässigt die Glieder über die vierte Potenz,... | |
 | William Chauvenet - Trigonometry - 1871 - 268 pages
...angles of the plane triangl* whose sides are a, b and c. Then we have, in the spherical triangle, , cos a — cos b cos c cos A = --- sin b sin c Substitute in the second member of this, the values of cos a, &c., in series, by PI. Trig. (405) and... | |
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A, 4 cos 6 = cos c cos a + sin c sin a cos B, > (1) . , "cos c = cos a cos b + sin a sin b cos C. J Whence . cos a — cos b... 
