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" A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B... "
Correspokndance sur l'École impériale polytechnique, par m. Hachette - Page 239
by Paris école polytechn - 1813
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Mémoires couronnés et autres mémoires publiés par l'Académie ..., Volume 15

Académie royale des sciences, des lettres et des beaux-arts de Belgique - Science - 1863
...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...
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Spherical Trigonometry: For the Use of Colleges and Schools

Isaac Todhunter - Spherical trigonometry - 1863 - 132 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')...
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Traité de cinématique

Jean-Baptiste-Charles-Joseph Bélanger - Kinematics - 1864 - 288 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...
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SPHERICAL ASTRONOMY

F. BRUNNOW - 1865
...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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Tratado elemental de trigonometria: escrito de Real Orden para uso de los ...

Saturnino Montojo - 1865 - 280 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 ,•...
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Spherical Astronomy ...

Franz Brünnow - 1865 - 560 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...
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A Collection of Elementary Test Questions in Pure and Mixed Mathematics with ...

James Robert Christie - Mathematics - 1866 - 404 pages
...adjacent parts. (2) Sine of middle part = product of cosines of opposite parts. In any spherical triangle, cos a= cos b, cos c — sin. b, sin c. cos A ; . . sin(*-6)sin(se) , sins, sin (*-a) Sin * A = - -. - ; - : - I COS * A = - T - . — : - : am b...
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Mathematical Exercises ...

Samuel H. Winter - 1867
...c cos A. Sin A : sin B : sin C : : sin a : sin b : sin c. Cot a sin b = cot A sin C + cos b cos C ; cos A = — cos B cos C + sin B sin C cos a. Sin i A = A / J»in(,-*)sin(,-C)) CQS ^ A = \/ \ sm b sin c } I /sin s sin (sa) \ ;tanJLA_ / ism (sb)am...
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A Book of Mathematical Problems on Subjects Included in the Cambridge Course

Joseph Wolstenholme - Mathematics - 1867 - 344 pages
...y" + a9 - 2ya cOS <f> i , 0+^ + ,/r=o prove that y3y sin 0 + ya sin <^> + a/3 sin if/ = 0. 297. If cos A + cos B cos C + sin B sin C cos A = 0, then will tan ^45° ± ^\ tan ^45" - |) tan ^45° - £) = - 1 ; and if cos A = cos B cos C ±...
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Elements of Trigonometry, Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 288 pages
...b' cos d -f sin V sin d cos A'. But sin a'=s!n A, cos a' = — cos A, sin b' = sin B, &c. Hence — cos A = cos B cos C + sin B sin C cos A ' From this equation we get for cos A' a value equal and with a contrary sign to that which equation...
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