 | Charles William Hackley - Trigonometry - 1851 - 536 pages
...3. Given B, c, and a to find A and b. The general relations between the given and required parts are cos A = — cos c cos B + sin c sin B cos a \ sin A cos 1 — sin c cos B .f- cos c ain B cos a '• (7)• sin A sin 6 = sin B ain a ) which determine A and... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...(s1n 6 cos A - s1n a cos /•) ; these equations may be placed under the forms, (1 - cos r) (cos a + cos b) = sin c (sin b cos A + sin a cos B), (1 + cos c) (cos a - cos 1) = sin c (sin b cos .A — sin a cos CZ> ) ; multiplying these equations,... | |
 | William Chauvenet - Trigonometry - 1855 - 264 pages
...between the given parts b, c, A and the required part a is expressed by the first equation of (4), cos a = cos c cos b + sin c sin b cos A (M) by which a may be found by computing separately the two terms of the second member and adding their... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...(sin 6 cos A — sin a cos B) , these equations may be placed under the forms, (1 — cos c) (cos a + cos b) = sin c (sin b cos A + sin a cos B), (1 + cos c) (cos a — cos b) = sin c (sin b cos A — sin a cos JB) ; multiplying these equations,... | |
 | William Chauvenet - Astronomical instruments - 1864 - 726 pages
...show as clearly as possible how the formula of Spherical Trigonometry are thus converted into formulae of Spherical Astronomy, let us first consider a spherical...quantities are [Sph. Trig. Art. 114]* cos a = cos c cos 6 + sin c sin b cos A , sin a cos B = sin c cos b — cos c sin b cos A > (01) sin a sin B = sin b... | |
 | William Chauvenet - 1864 - 720 pages
...show as clearly as possible how the formuhe of Spherical Trigonometry are thus converted into formulae of Spherical Astronomy, let us first consider a, spherical...which there are given the angle A, and the sides b and <?, to find the angle B and the side a. The general relations between these five quantities are [Sph.... | |
 | William Chauvenet - 1875 - 270 pages
...substituting the values of the co-ordinates, we have at once the three following 'indamental equations: cos a = cos c cos b -\- sin c sin b cos A } sin a cos It = sin e cos b — cos c sin b cos -I !• (N) sin a sin В = sin li sin Л ) which are identical... | |
 | Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...cose = cos6 cosa + sin6 sina cosC. From the relation PP a' 7= "' 7 may be deduced in like manner — cos A = cos c cos B — sin c sin B cos a. 8. Resuming the equation y ay of the last example, and taking the vectors, we have [Equation (91)],... | |
 | John Butler Johnson - Engineering - 1886 - 724 pages
...//. FlG" "' Taking the parenthetical notation of the figure, we have, from spherical trigonometry, cos (a) = cos (c) cos (b) + sin (c) sin (b) cos (A). But in terms of d, 0, k, and A, this becomes sin d = sin 0 sin h — cos 0 cos h cos A, . . . (i) In... | |
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A, and the sides b and c, to find the angle B and the side a. The general relations between these five quantities are [Sph. Trig. Art. 114]* cos a = cos c cos b -\- sin c sin b cos A | sin a cos B = sin c cos b — cos c sin b cos A... 