 | James Robert Christie - Mathematics - 1866 - 428 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... | |
 | Benjamin Greenleaf - 1867 - 188 pages
...angle, 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... | |
 | Samuel H. Winter - 1867 - 468 pages
...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... | |
 | Joseph Wolstenholme - Mathematics - 1867 - 368 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 ±... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 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... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...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... | |
 | William Rossiter - 1868 - 186 pages
...(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... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...thence, . /— cos $S cos (4-iS— A) tan £a = \/ * 4l~^ — 7n V cos US— B) cos (i*3— C) 83. From Equation ( 1 ), Art. 80, we have, cos A + cos B cos C = sin B sin (7 cos a = sin (7 -: — — sin 6 cos a : s1n 05 (1.) since, from Proportion ( 1 ), Art. 78, we have,... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...Applying (150) to A'BC1, we have cos a' = cos If cos ci -\- sin V sin c1 cos A' ; or, by (46), — cos A = cos B cos C — sin B sin C cos a ; whence, cos A = sin B sin C cos a — cos B cos i7. (153) In like manner may be deduced cos B= sin... | |
 | Mathematics - 1869 - 124 pages
...pt = tan Ci tan c2 = tan b tan c cos A tan p2 = sin o, tan B, = tan p cot B cot C sec a, sin b sin c cos A cos B cos C sin B sin C cos a cos b cos c ' therefore, at once, tan3 k = — which, substituting for the functions of the angles... | |
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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. 
