 | Jean-Baptiste-Charles-Joseph Bélanger - 1864 - 348 sivua
...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... | |
 | Franz Brünnow - 1865 - 592 sivua
...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... | |
 | Saturnino Montojo - 1865 - 302 sivua
...sin' C = 0, y poniendo en el último término por sin b sin C su equivalente sin B sin c, resulta . cos A = — cos B cos C + sin B sin C cos a : relacion entre los tres ángulos y un lado análoga á la («a,i) 5 y de la cual hubiera podido deducirse... | |
 | Franz Brünnow - 1865 - 584 sivua
...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... | |
 | James Robert Christie - 1866 - 428 sivua
...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... | |
 | Benjamin Greenleaf - 1867 - 188 sivua
...plus the jcosine 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 sin C sin a -. — j. sin A Substituting... | |
 | Joseph Wolstenholme - 1867 - 368 sivua
...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 ±... | |
 | Samuel H. Winter - 1867 - 468 sivua
...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... | |
 | William Rossiter - 1868 - 186 sivua
...(axb) ' = coi Ç «fa * С"~6) 2 si» à (a + 6) (8.) coi a si-» c = cos c cos В + sin В coi A. For, cos a = cos b cos c + sin b sin c cos A ; also, cos 6 = cos c cos a + sin c sin a cos В ; substituting the value of cos b for cos b, in the... | |
 | Eli Todd Tappan - 1868 - 432 sivua
...cos. (180°— A) = cos. (180° — B) cos. (180° — C) + Reducing (829), and changing the signs, cos. A = — cos. B cos. C + sin. B sin. C cos. a. Similarly, cos. B = — cos. A cos. C -j- sin. A sin. C cos. b, cos. C = — cos. A cos. B + sin. A... | |
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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... 
