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" A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B... "
Correspokndance sur l'École impériale polytechnique, par m. Hachette - Page 239
by Paris école polytechn - 1813
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Elements of Plane and Spherical Trigonometry with Logarithmic and ..., Volume 1

Simon Newcomb - Logarithms - 1882 - 168 pages
...the fundamental equations of spherical trigonometry, because by means of them, when three parts are cos a = cos b cos c + sin b sin c cos A ; •] cos b — cos c cos a -|~ sin c sin a cos 2?} > (1) given, the other three may be found. For...
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Gesammelte Abhandlungen

G. Kirchhoff - Physics - 1882 - 641 pages
...auch x und x gemessen hat. Bezeichnet man den Bogen MN durch b und den Winkel durch A, so hat man: [ cos a = cos b cos c + sin b sin c cos A \ cos «'= cos b cos c — sin b sin r cos A oder l a' + a a' — o <4> l . , . i . «+a. .-. sin o...
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Mémoires de l'Académie des sciences, inscriptions et belles-lettres de Toulouse

Académie des sciences, inscriptions et belles-lettres de Toulouse - Literature - 1883
...sur une sphère d'un rayon égal à l'unité, qui aurait pour centre le point M. Ce triangle donne : cos a = cos b cos c + sin b sin c cos A ; et puisque la droite MN est perpendiculaire à MT, onac = |. de sorte que la formule précédente...
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Briefwechsel

Carl Friedrich Gauß - Mathematicians
...findet : tang B2 + tang C2 — 2 tang /, tang C cos a = sec B2 + scc C2 — 2 sec R scc C cos A oder cos A = cos B cos C -\- sin B sin C cos a usw Hieraus leitete ich , dadurch dass ich aus diesen Gleichungen sin a, sin b, sin e bestimmte, sin...
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The Cambridge history of Islam: Islamic society and civilization. Vol. 2B

Peter Malcolm Holt, Ann K. S. Lambton, Bernard Lewis - Islam - 1977 - 523 pages
...(uniting the three sides and one angle of a spherical triangle) which has no equivalent in Ptolemy: cos a = cos b cos c — sin b sin c cos A A further advance was made with Abu'1-Wafa', and he was probably the first to demonstrate the sine...
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Astronomie de position, géodésie

André Caillemer, Catherine Le Cocq - Geodesy - 1983 - 264 pages
...tirer d'affaire en toutes circonstances, sans le secours d'imprimés qui risquent de faire défaut cos a = cos b cos c + sin b sin c cos A et : sin a sin b sin A sin B sin C Dans le triangle de position ces formules donnent : cos z = sin...
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Robot Vision

Berthold Horn, Berthold Klaus, Paul Horn - Computers - 1986 - 509 pages
...for the sides is cos a = cos 6 cos c + sin 6 sin c cos A, while the law of cosines for the angles is cos A = - cos B cos C + sin B sin C cos a. There are two more formulae in each case obtained by simultaneous cyclical permutation of a, 6, c and...
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Mathematical Modelling

Jagat Narain Kapur - Mathematical models - 1988 - 259 pages
...triangles are given by sin A sin B sin С .... —. = — — г = — : (25) sin a sin b sin c and cos a = cos b cos c + sin b sin c cos A (26) The point vertically above the observer is called his zenith and is denoted by Z. Thus OZ gives...
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Differential Geometry

J. J. Stoker - Mathematics - 1989 - 432 pages
...triangle T**. The "law of cosines " for triangles in each of the three geometries of constant curvature is cos a = cos b cos c + sin b sin c cos a (K* > 0), a* = b* + c2 - 2bc cos a (K* = 0), cosh a = cosh 6 cosh c — sinh b sinh c cos a (K* < 0)....
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Engineering Mathematics and Statistics: Pocket Handbook

Nicholas P. Cheremisinoff, Louise Ferrante - Mathematics - 1989 - 200 pages
...spherical triangle and A, B, C represent the corresponding opposite angles Law of Cosines for Sides 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 Law of Tangents tan...
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