 | Harvard University - 1873 - 732 pages
...Obtain the first two formulas used in the previous question, by means of the following equations: — cos a = cos b cos c + sin b sin c cos A, k sin <(> = sin ft cos A, k cos # = cos 6. 7. Given in a spherical oblique triangle, B = 22° 48',... | |
 | Charles Davies - 1874 - 464 pages
...— -. — ^ - • • • (2.) V s1n B sm C and thence, /— cos ±8 cos (±S — A) tan *a = 83. From Equation ( 1 ), Art. 80, we have, cos A + cos...cos C — sin B sin C cos a = sin C -. - sin b cos a ; s1n a (1.) since, from Proportion ( 1 ), Art. 78, we have, . n am A sm B = .: - s1n o. s1n a Also,... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...S- /?) cos(i^-C') cos - ^— — " - ' sin -Z? sin C ' and thence, — cos A,S cos ( AS — A ) 83. From Equation ( 1 ), Art. 80, we have, cos A + cos B cos C = sin -Z? sin (7 cos a = sin (7 .= - sin b cos a : sm a (!•) since, from Proportion ( 1 ), Art. 78, we... | |
 | Electronic journals - 1882 - 452 pages
...sin2a and transposing, 1 — cos a cos b cos c = sin* a + sin b sin c cos A cos a; (1) also cosM = — cos A cos B cos C -\- sin B sin C cos a cos A, whence 1 + cos A cos B cos C '= sin1 A + sin B sin Ccos acos A. (2) Dividing (2) by (1), we... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...differing more from 90° than another side is of the same species as its opposite angle. By article 136, we have cos a = cos b cos c + sin b' sin c cos A. cos a — cos b cos c cos A = sin 6 sin c But sin 6 sin c is positive, since ¿> and c are each less... | |
 | Karl Wilhelm Unverzagt - Quaternions - 1876 - 342 pages
...Scalarund Vectortheil. Uebersetzt lautet die Gleichung cos a = cos c cos b + sin c sin b S (oq . obi), oder cos a = cos b cos c -|- sin b sin c cos A, da S (oc, . ob, ) = — cos (n — A) = cos A ist. (II.) Um den SinussUtz sin a : sin b = sin A : sin... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 204 pages
...cos AD sin c cos b sin AD . • . cos a = I . cOS AD cOS AD and from [3] tan AD = cos A tan b ; . . . cos a = cos b cos c + sin b sin c cos A, and similarly cos b = cos c cos a + sin c sin a cos B, cos c = cos a cos b + sin a sin 6 cos C. NOTE.... | |
 | Samuel H. Winter - 1877 - 452 pages
...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. S, / fsin (* — b) sin (s — c)| , ln 2 A = A / i • A • f * cos 1 A = ^/ ( sin o sin c J / f... | |
 | Rehuel Lobatto - Trigonometry - 1877 - 382 pages
...Sin Q rz — cos B cos C + cos B sin G cotQ. Maar in A DCB , cot Q — cos a <a«^ B zijnde , wordt cos A = — cos B cos C + sin B sin C cos a ; . . (4) zoodat nu, na behoorlijke verwisseling van letters, alle grondformulen terug zijn gevonden.... | |
 | Henry Nathan Wheeler - Plane trigonometry - 1878 - 198 pages
...the triangle A'B'C' we get cos a' = cos b' cos d + sin V sin d cos A', or substituting from above — cos A = (— cos B) (— cos C) + sin B sin C (— cos a) ; or — cos A = cos B cos C — sin B sin C cos a, ) and similarly I r-*r>-, ™ T. ri -ni COS ^ —... | |
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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. 
