 | William Thomas Read - 1862 - 144 pages
...2 OP . OE, OD . OD PD . DE . c0sa = op7oE + pcrroE-cosA = cos b . cos c + sin b . sin c cos A ; and cos a — cos b . cos c = sin b . sin c cos A. Therefore f*>»«-«»ft•«>•« = cos A. sin b . sin c NB — Compare this with the value of cos... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...- cos A', sin. (180° -jB') = sin B\ <fcc., we have, — cos A' = cos B' cos (7' — sin B' sin (7' cos a' ; or, changing the signs and omitting the primes...(since the preceding result is true for any triangle), In the same way, we may deduce, cos J5 = sin A sin C cos b — cos A cos C • (2.) cos C = sin ^t... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...angle, plus the cosine of the second side into the cosine of the included angle. By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b -|- sin a sin b cos (7; and by means of (147), sin c sm a sin C sin A* , . ^ 7... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...therefore, cos a = -^OC* + ~W "* A' ' Substituting the functions derived from the triangles 0 A' O A' O, we have cos a = cos b cos c -)- sin b sin c cos A. In like manner may be deduced cos b = cos c cos a -)- sin c sin a cos B, cos c = cos a cos b -)- sin... | |
 | Académie royale des sciences, des lettres et des beaux-arts de Belgique - Science - 1863 - 702 pages
...on représente par A, B, C les angles et par «, 6, B c les côtés opposés, la formule générale cos A = — cos B cos C + sin B . sin C . cos a , où l'on doit poser C = 90°, donne cos A = sin B . cos «. On a, d'ailleurs, r cos a — — > sin... | |
 | Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...base and A the opposite angle of one triangle, arid a and A' similar quantities for the other. Then cos a = cos b cos c + sin b sin c cos A, cos a' = cos b cos c + sin b sin c cos A'; therefore cos a - cos a' = sin b sin c (cos A — cos A')... | |
 | Jean-Baptiste-Charles-Joseph Bélanger - Kinematics - 1864 - 348 pages
...trois angles plans a, b, e d'un angle dièdre et de l'angle dièdre A opposé à la face a, . savoir : cos a = cos b cos c + sin b sin c cos A en faisant « = T, 6 = « et c = j3+-, ce qui donne 0 = —cos y. sin j3 -f- sin a. cos j3 cos A, d'où... | |
 | Saturnino Montojo - 1865 - 302 pages
...Q,6a= 90°. De esta fórmula («) podremos ya deducir por la permutacion indicada (39) las siguientes cos a = cos b cos c + sin b sin c cos A \ cos b = cos c cos a + sin c sin a cos B > («, „) cos c = cos a cos b + sin a sin b cos C ,•... | |
 | Franz Brünnow - 1865 - 592 pages
...we have found in No. 2, we get the following formulae, which are true for every spherical triangle : cos a = cos b cos c + sin b sin c cos A gin a sin B = sin .•'• sin I sin o cos-B= cosi sin r. — sin i cos c cos A. These are the three... | |
 | Franz Brünnow - 1865 - 584 pages
...we have found in No. 2, we get the following formulae, which are true for every spherical triangle : cos a = cos b cos c -+- sin b sin c cos A sin a sin 5 = sin b sin, A sin a cos B = cos b sin c — sin b cos c cos A. These are the three principal... | |
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A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a. 
