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" B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G. "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 138
by Nathan Scholfield - 1845 - 232 pages
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Zeitschrift für Mathematik und Physik, Volume 6

Mathematics - 1861 - 596 pages
...cos b — sin a sin b cos R. Nach einer bekannten Grundformel der sphärischen Trigonometrie ist aber cos c = cos a cos b + sin a sin b cos C, folglich cos R = — cos C; di R = 180 — C. Ferner ist nach Principien der ebenen Trigonometrie cos...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1861 - 396 pages
...(298), cos. a tang. CP= cos. C tang, a cos. a = cos. C sin. a ; (304) which, substituted in (303), gives cos. c = cos. a cos. b -|- sin. a sin. b cos. C. (305) Since c and C may denote any side and its opposite angle, we have also cos. a = cos. b cos. I...
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The Mathematical Monthly, Volume 3

John Daniel Runkle - Mathematics - 1861 - 436 pages
...— C) =. cos(?r — A) COS(TT — B) -\- sin (TT — A) X sin(?r — B) COS(TT — c), that is, — cos C = cos A cos B — sin A sin B cos C ; and now, if the spherical triangle ABC be rightrangled at C, that is, if C= 90°, these two equations...
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Elemente der Vermessungskunde

Carl Maximilian von Bauernfeind, Karl Maximilian von Bauernfeind - Scientific apparatus and instruments - 1862 - 874 pages
...findet folglich den Winkel A',CB'=C' = y' aus der bekannten Grundformel der sphärischen Trigonometrie: cos c = cos a cos b + sin a sin b cos C, wenn man darin a = 90° — /#, b = 90° — a, c = y und C = y' setzt. Nach dieser Substitution und...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...cosine of the included angle. By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b -\- sin a sin b cos C; and by means of (147), sin C sin c = sin a --. — -.. sin A . , „. , . sin a sin b cos A sin C cosa...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...cosine of the included angle. By (150) and (152) we have cos a = cos b cos c -j- sin b sin c cos A, cos c = cos a cos b -]" sin a sin b cos C; and by means of (147), sin C sin c = sm a . — 5. am A Substituting these values of COS e and sin...
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Popular and Mathematical Astronomy, with the principal formulæ of Plane and ...

William Thomas READ - 1862 - 144 pages
...triangle, and the included angle, to find the third side. Let a, b, and angle C be given. Kg. 21. Since cos c = cos a cos b + sin a sin b . cos C, and cos C = (2 cos2 -^ — 1); therefore, Q cos c = cos a cos b + sin a sin b . (2 cos2 -~ 1) 0 = cos...
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Spherical Trigonometry: For the Use of Colleges and Schools

Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...free from ambiguity. Or we may determine C without previously determining a and b from the formula cos C = — cos A cos B + sin A sin B cos c. This formula may be adapted to logarithms, thus; cos C = cos B (— cos A + sin A tan B cos c) ; assume...
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Tratado elemental de trigonometria: escrito de Real Orden para uso de los ...

Saturnino Montojo - 1865 - 302 pages
...(39) las siguientes cos a = cos b cos c + sin b sin c cos A \ cos b = cos c cos a + sin c sin a cos B > («, „) cos c = cos a cos b + sin a sin b cos C ,• en las cuales como se hallen relacionados entre sí t<w dos los elementos del triángulo en toda...
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Lehrbuch der physikalischen Mineralogie, Volumes 1-2

Albrecht Schrauf - Crystallography - 1866 - 762 pages
...cotg v» 2. Bekannt ab G sin c sin B = sin ft sin C sin c cos J? = sin a cos b — cos a sin b cos (7 cos c = cos a cos b -\- sin a sin b cos C cotg a sin ft — cos b cos C „ cotg b sin a — cos a cos C B = - ! - ; - f= -- sin G ÜUS /2 -A...
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