 | James Morford Taylor - Trigonometry - 1905 - 256 pages
...A . (5) Substituting in (3) for cos AD cosp and sin AD cosp their values in (4) and (5), we obtain cos a = cos b cos с + sin b sin с cos A. [42] Similarly, or by symmetry from [42], we have cos b = cos с cos a + sin с sin a cos B, cos e... | |
 | Friedrich Gauss - 1906 - 394 pages
...о. 2. Das schiefwinklige sphärische Dreieck. JITJ U (49) sin a sin a tin b sin ß sin с sin (50) cos a = cos b cos с + sin b sin с cos a. (51) cos Ь = caí a cos с 4- sin a sin с cos ß. ( 5Z ) cos с = cos a cos b + sin a sin b cos y.... | |
 | William Carpenter Pendleton Muir - Nautical astronomy - 1906 - 754 pages
...azimuth to find the variation in / di to a variation in h. Taking the fundamental trigonometric formula cos a = cos b cos с + sin b sin с cos A, ein A sin b = sin B sin a, and substituting A = Z, B = M, a = 90° — d, b = 90° — с = 90 —... | |
 | William Charles Brenke - Algebra - 1910 - 374 pages
...Triangles. (317-22.) Law of Sines : sin a : sin b : sin с = sin A : sin В : sin C. Law of Cosines: cos a = cos b cos с + sin b sin с cos A. Half-Angles. 1 ,,,,., t sin (s — a) sin (s — 6) sin (s — c) S = = - - - i - 14. sin о sin 1... | |
 | Robert Édouard Moritz - Trigonometry - 1913 - 562 pages
...that OF2 — EF2 = OE2, OG2 — EG* = OE2, we find that which, on dividing by 2 OF • OG, leads to cos a = cos b cos с + sin b sin с cos A . This constitutes & fourth proof of the law of cosines. 6. From the law of cosines cos A = (cos a... | |
 | George Wentworth, David Eugene Smith - Trigonometry - 1915 - 388 pages
...parts. PRINCIPAL FORMULA8 OF OBLIQUE TRIANGLE8 (§§ 189-191) sin a _ sin b _ sin с sin Л sinВ sin C cos a = cos b cos с + sin b sin с cos Л. cos b = cos с cos a + sin с sin a cos В. cos с = cos « cos b + sin a sin ¿ cos C. cos Л... | |
 | Herbert Bell - Spherical trigonometry - 1915 - 86 pages
...Emerson-Langley Construction. — We shall next describe a second method for solving graphically the equation cos a = cos b cos с + sin b sin с cos A, which is due to W. Emerson (1701-1782) and EM Langley.* Draw a circle XPX'R of unit radius (fig. 14)... | |
 | Edward Vermilye Huntington, Louis Albert Fischer - Engineering - 1916 - 196 pages
...(See also p. 100.) sin a sin b sin b sin с sin с sin a sin Л sin Л' sin .В sin С' ein С sin Л cos a = cos b cos с + sin b sin с cos A, with similar formulas for cos b and cos c. cos A = — cos В cos С + sin В sin С cos a, with similar... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...------ — - — ¿t S —* d [43] A = Vs(sa)(sb)(sc). [441 sina _ sinff _ Sin7 sin a sin b sin с [45] cos a = cos b cos с + sin b sin с cos a. [46] cos a = — cos ß cos 7 + sin ß sin 7 cos о. , , .. l . /sin (s — b) sin (s — c) , !471sin2"=V... | |
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By equating the results and transposing, cos a = cos b cos с — sin b sin с cos A cos b... 
