 | Werner Fenchel - Geometry, Hyperbolic - 1989 - 248 pages
...(n-ß)i, <T2 = (ny)i. Hence, (3) takes the form sin a sin b sin c sin a sin ß sin y ' and (6) yields cos a = cos b cos c + sin b sin c cos a , and the analogues for cos b and cos c, cos a = — cos ß cos y + sin ß sin y cos a , and the analogues... | |
 | 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).... | |
 | Morris Kline - Mathematics - 1990 - 434 pages
...triangles, namely, TRIGONOMETRY A Figure 12.1 and the law of cosines involving the sides, that is, cos a = cos b cos c + sin b sin c cos A. The De Triangulis was not published until 1533; in the meantime, Johann Werner (1468-1528) improved... | |
 | C. M. R. Fowler, Clarence Mary R. Fowler, Mary Fowler - Science - 1990 - 494 pages
...relate the angles and sides of plane triangles, there are cosine and sine rules for spherical triangles: cos a = cos b cos c + sin b sin c cos A (2.9) and sin a sin c sin A sin C Substituting Eqs. 2.4-2.6 into Eq. 2.9 gives (2.10) cos a = cos (90... | |
 | Lancelot Hogben - Mathematics - 1968 - 662 pages
...— sin2 x First, however, you should notice that if we can get a when b, c, and A are known from: cos a = cos b cos c + sin b sin c cos A we can also get c when a, b, and C are known from cos c = cos a cos b + sin a sin b cos C The demonstration... | |
 | P. Boulanger, M.A. Hayes - Mathematics - 1993 - 300 pages
...is when one of the angles is ¿я. AI Arbitrary triangles First we derive the fundamental formula: cos a = cos b cos c + sin b sin c cos A. (A. 1 ) Proof: Take the radius of the sphere to be of unit length. Let a be the plane passing through... | |
 | Bruno Pattan - Technology & Engineering - 1993 - 420 pages
...Law of Cosines for sides: cos a - cos b cos c + sin b sin c cos A o The Law of Cosines for angles: cos A = - cos B cos C + sin B sin C cos a o The Law of Sines: sin A . sin B _ sin C sin a sin b sin c o Napier's Rules of Circular Parts (for... | |
 | Friedrich Seck - Science - 1995 - 332 pages
...mit dem aus den drei Seiten (a, b, c) des sphärischen Dreiecks der Winkel a berechnet werden kann: cos a = cos b - cos c + sin b - sin c - cos a, ergibt sich durch Umformung: cos a — cos b - cos c .c , \ cos a = (Formel i) sin b - sin c Die trigonometrischen... | |
 | A. Gardiner, Anthony Gardiner - Mathematics - 1997 - 252 pages
...string does not lie in a plane if tan 6>r/h. [Note: You may assume spherical triangle formulae such as cos a = cos b cos c + sin b sin c cos A , or sin A cot B = sin c cot b - cos c cos A . In a spherical triangle the sides a, fo, and c are arcs of... | |
 | Jan Gullberg - Mathematics - 1997 - 1148 pages
...Triangle The law of cosines concerning angles of a spherical triangle is here quoted without proof: cos A = - cos B cos C + sin B sin C cos a cos B = - cos C cos A + sin C sin A cos 6 cos C = — cos A cos B + sin A sin B cos c FINCKE Thomas... | |
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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... 
