 | Edward Albert Bowser - 1892 - 392 pągines
...s', m — 'ii' , „a — b tan tan — i : — = tau2 •• 62. Prove sin 6 sin с + cos b cos с cos A = sin B sin C — cos B cos C cos a. 63. Show that the arc l joining the middle points of the two sides a and 6 of a triangle is thus given... | |
 | William John McClelland, Thomas Preston - 1893 - 402 pągines
...— *'. a -<r' a - 1 tan — — - tan — — = tan2 — — AA 2 2. Prove that sin b sin c + cos b cos c cos A = sin B sin C- cos B cos C cos «. [If from the extremities of the base BC quadrants CO' and BB' be measured on the sides towards... | |
 | John Bascombe Lock - 1896 - 244 pągines
...+ sin c sin a cos B, > (1) . , "cos c = cos a cos b + sin a sin b cos C. J Whence . cos a — cos b cos c cos A = ; ; , sin b sin c cos b — cos c cos a cosB = cos С — sm c sin a. cos c — cos a cos b f2) The last two formulae of either set can be... | |
 | Nikolaĭ Ivanovich Lobachevskiĭ - 1898 - 510 pągines
...-f- cos b cos c = cos a sin a sin B = sin b sin A cot .4 sin C + cos C cos ft — cot a sin ft = 0 cos a sin B sin C — cos B cos C = cos .a. Die Messung der sphärischen Dreiecke hängt folglich nicht von der Annahme über die Parallelen ab.... | |
 | William Chauvenet - 1901 - 278 pągines
...have sin 6 sin c sin' A = sin 7J sin Csin2 a, these two' equations give, sin 6 sin c + cos 6 cos e cos A = sin B sin C — cos B cos C cos a ( 78) a relation between the six parts of the triangle, (irst given by CAONOLI. It is a property of... | |
 | George Albert Wentworth - 1903 - 346 pągines
...equation of [46], p. 160, cos B cos C + cos A COS a = - ; - : - • • sin B sin C Therefore, 1 — COS a = - : - : sin B sin C — cos B cos C — cos A sin B sin C — cos (B + C) — cos A by [5], p. 54, = ---- sinjjs / c by [22], p. 59, = JLJ and 1... | |
 | 1911 - 1124 pągines
...These formulae were given by Schmicsser in Crclle's Journ., vol. x. The relation sin b sin c+cos b cos c cos A «=sin B sin C— cos B cos C cos a was given by Cagnoli in his Trigonometry (1786), CmmAirm an<* was rediscovered by Cayley (Phil. Mag.,... | |
 | Leonard Magruder Passano - 1918 - 176 pągines
...cosines cos a — cos b cos c cos .4 = Whence 1 — cos A _ sin b sin c + cos b cos c — cos a 1 + cos A sin b sin c — cos b cos c + cos a _ cos (b — c) — cos a _ cos a — cos (b — c) cos a — cos (6 4- c) cos (b + c) — cos a But... | |
 | 1859 - 520 pągines
...triangle, if as usual a, b, c are the sides, and A, B, C the opposite angles, then sin b sin c + cos b cos c cos A = sin B sin C — cos B cos C cos a, sin c sin a + cos c cos a cos B = sin C sin A — cos C cos A cos b, sin a sin b + cos a cos b cos... | |
| |
Shew that sin b sin c + cos b cos c cos A = sin B sin C 
