 | William Wallace Campbell - 1899 - 288 pàgines
...Chauvenet's jSph. Trig., § 114] the general equations cos a — cos b cos c + sin b sin c cos A, (1) sin a cos B = cos b sin c — sin b cos c cos A, (2) sin a sin B = sin b sin A. (3) To adapt these equations to the triangle POZ, let A * PZO = 180°... | |
 | George Cary Comstock - 1903 - 254 pàgines
...obtain the following relations among the sides and angles of the triangle : sin a sin B = sin b sin A , sin a cos B =cos b sin c — sin b cos c cos A, (4) cos a = cos b cos c + sin b sin c cos A . These are the fundamental equations of spherical trigonometry... | |
 | Robert Stawell Ball - 1908 - 528 pàgines
...cos b sin c cos A&b + sin 6 cos c cos A Ac — sin b sin c sin A&A. But from the formula (2) in § 1 sin a cos B = cos b sin c — sin b cos c cos A, sin a cos C = sin b cos c — cos 6 sin c cos A ; whence by substitution, and writing the similar formulae... | |
 | Hugo Buchholz - 1908 - 470 pàgines
...durch Projektion von B auf die Ebene AOC erhalten werden: cos a = cos b cosc + sin 1> cos c cos A , sin a cos B = cos b sin c — sin b cos c cos ^ , (IV) sin a sin -Z? = sin i sin A , sin a cos C = sin 3 cos c — cos 4 sin c cos ^ , sin a sin... | |
 | Hugo Buchholz - 1908 - 496 pàgines
...Projektion von B auf die Ebene AOC erhalten werden: Fig. 136. cos a = cos b cosc + sin b cos c cos A , sin a cos B = cos b sin c — sin b cos c cos // , (IV) sin a sin B = sin A sin A , sin a cos C = sin Ä cos c — cos Ä sin c cos // , sin a sin... | |
 | George Leonard Hosmer - 1910 - 260 pàgines
...The fundamental formulae of spherical trigonometry are cos a = cos b cos c + sin b sin c cos A, [5] sin a cos B = cos b sin c — sin b cos c cos .4 , [6] sin a sin 5 = sin b sin ^4. [7] % If we put A = P, B = S, C = Z, a = 90° - h, b = g0° -... | |
 | Andrew Hall Holt - 1916 - 152 pàgines
...x, y, z, x't y', z', and dividing by r, we have: cos a = cos b • cos c + sin b • sin c • cos A sin a • cos B = cos b • sin c — sin b • cos c • cos A sin a • sin B = sin b • sin A which are the three Fundamental Laws of Spherical Trigonometry. Since... | |
 | William Carpenter Pendleton Muir - 1918 - 814 pàgines
...— cos d cos < sin L we have -?-/• = 3 ? — = — : ' dL COP a cos Z/ sin t From trigonometry, sin a cos B = cos b sin c — sin b cos c cos 4. Ut = A,B = Z,a = 90e — h,b = 00° — d, c = 90° — L, by substitution, we have cos h cos Z... | |
 | Lancelot Minor Berkely - 1924 - 98 pàgines
...hdh dh _ cos A cos <p — sin A s'm <p cos h d<P ~ sin A cos <p sin h In any spherical triangle ABC, sin a cos B = cos b sin c — sin b cos c cos A. Applying this formula to the triangle PZS, sin ZS cos PZS = cos PS sin PZ — sin PS cos PZ cos ZPS,... | |
 | George Leonard Hosmer - 1925 - 306 pàgines
...small letter. For example, the first two equations would be cos A = cos B cos C + sin B sin C cos a (a) sin A cos b = cos B sin C — sin B cos C cos a. (b) There will also be two other sets of equations for the angles B and C. Equation (1) may be regarded... | |
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A sin a cos B = cos b sin c —• sin b cos c cos A. 
