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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... "
An Elementary Treatise on Plane & Spherical Trigonometry: With Their ... - Page 172
by Benjamin Peirce - 1845 - 449 pages
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Surveying

B. C. Punmia - Photogrammetry - 2005 - 304 pages
...Also, sin A cos A = sin B sin C cos a - cos b cos c sin b sin c cos a = cos b cos c + sin b sin c cos A cos A = - cos B cos C + sin B sin C cos a ...(1.1) ...(1.2) ...(1.3) A \l sin (s — b) sin (s — c) ,, .. sin— = V : — — ...(1.4) 2 sin...
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Fundamentals of Astronomy

C Barbieri - Science - 2006 - 388 pages
...relation, and a variant of the first formula we shall apply are: cos a cos C = sin a cot b - sin C cot B, cos A = -cos B cos C + sin B sin C cos a where "cot" means "I/tan" (not the inverse tan!). Analogous to Brigg's formulae are the following (2s...
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Elliptic Functions

J. V. Armitage, W. F. Eberlein - Mathematics - 2006
...underlying principle is called the duality principle. In particular (for example) (9.56) may be replaced by cos A = — cos B cos C + sin B sin C cos a, (9.57) and similar expressions are obtained by cyclic interchange. 9.6.2 Elliptic functions and spherical...
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Introduction to Mathematical Modeling of Crop Growth: How the Equations are ...

Christopher B. S. Teh - Technology & Engineering - 2006 - 277 pages
...as points A and C are along the lines OA and OE, respectively. Finally, Eq. B.2 is re-expressed to cos a = cos b cos c + sin b sin c cos A Similarly, using the above principles, it can be shown that cos b = cos c cos a + sin c sin a cos B...
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Riemannian Geometry

Peter Petersen - Mathematics - 2006 - 405 pages
...a. Then, ip (t) = Ci cos t + C2 sin t + I = (v?(0)- 1) cost + v?'(0) sin i+1, and consequently 1 — cos a = — cos b cos c — sin b sin c cos a + I , which implies the law of cosines. D The proof of the law of cosines suggests that in working...
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Solar System Astrophysics: Background Science and the Inner Solar System

Eugene F. Milone, William J.F. Wilson - Science - 2008 - 258 pages
...The Law of Cosines for a Spherical Triangle In this section we demonstrate a proof of the cosine law: cos a = cos b cos c + sin b sin c cos A First, we derive some useful results for a right spherical triangle (ZC = 90 in Figure 2.3), which...
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