 | Richard Cohen - Science - 1998 - 226 pages
...sin b sine ' cosacos(6-#) cos c = cos a cos o + sm a sin o cos C = , COS0 where tan 9 = tan a cos C, cos C = — cos A cos B + sin A sin B cos c. 8.11 Inverse trigonometric functions Series Expansions: arcsm x = x + — — + l-3x5 2-3 2-4-5 X3... | |
 | Jan Gullberg - Mathematics - 1997 - 1148 pages
...Law of Cosines for Spherical Triangles Sides of a Spherical Triangle For spherical triangles, we have cos c = cos a cos b + sin a sin b cos C . where sides a, 6, and c, being arcs of great circles, are measured by their subtended central angles.... | |
 | William P. Thurston - Mathematics - 1997 - 340 pages
.../.(wi,Wj). We obtain, for example, COS 012 = COS Z (wiiWz) = COS 02 COS 01 + COS 03 sin 02 sin 0i or cos C = — cos A cos B + sin A sin B cos c. Exercise 2.4.4. In the limiting case of a very small triangle, we should be able to recover formulas... | |
 | A.I. Lurie - Computers - 2002 - 878 pages
...formulae corresponding to the above geometric construction. We will use formulae of spherical trigonometry cos c = cos a cos b + sin a sin b cos C, (3.3.2) sin a sin b sin c sin A sin B sin C (3.3.3) cos C = — cos A cos B + sin A sin B cos c, (3.3.4)... | |
 | James B. Kaler - Nature - 2002 - 524 pages
...trigonometry: cos a = cos b cos c + sin b sin c cos A, (3) cos b = cos a cos c + sin a sin c cos B, cos c = cos a cos b + sin a sin b cos C. The spherical triangle. Spherical triangle ABC is constructed from the arcs of three intersecting great... | |
 | François Bréhat, Bruneau Wyncke - 2003 - 248 pages
...et c : cos a = cos b cos c + sin b sin c cos A (TS3a) cos b = cos c cos a + sin c sin a cos B (TS3b) cos c = cos a cos b + sin a sin b cos C (TS3c) Loi des cosinus pour les angles A, B et C : Cette loi est établie en appliquant la loi des... | |
 | Philippe de Maeyer, Beata M. de Vliegher, Marijke Brondeel - 2004 - 391 pages
...geldt de cosinusregel: 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 in een boldriehoek met de hoekpunten A, B en C en resp. zijden a, b en c geldt de sinusregel: sin a... | |
 | Luke Hodgkin - Mathematics - 2005 - 302 pages
...C would give us ß if we knew c. since we know b and C. But we can get c from the 'cosine formula': cos c = cos a cos b + sin a sin b cos C (See Gray 1978. p 46) North pole (C) Angle C Us <B) 1 0. It is easy to check that the vertices given... | |
 | Schuyler Erle, Rich Gibson, Jo Walsh - Computers - 2005 - 564 pages
...theorem to triangles that lack a right angle. The Law of Cosines for spherical trigonometry states that: cos c = cos a cos b + sin a sin b cos C In this relation, C is the angle between edges a and b on a "triangle" connecting three points on a... | |
 | J. V. Armitage, W. F. Eberlein - Mathematics - 2006 - 9 pages
...By differentiating the result obtained from (9.54) by cyclic interchange (namely the polar formula cos C = —cos A cos B + sin A sin B cos c), show that (sin A cos B + cos A sin B cos c)dA + (cos A sin B + sin A cos B cos c)dZ? = 0, and then... | |
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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. 
