 | 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.... | |
 | 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 ^ —... | |
 | Isaac Todhunter - Spherical trigonometry - 1879 - 176 pages
...quadrants. Produce AB and AC to meet at A' ; put = c', A'C = V; then from the triangle ABC, as before, cos a = cos b' cos c' + sin b' sin c' cos A'; but b'-тг — b, c' = тг-c, A' — A; thus cos a = cos 6 cos с + sin 6 sin с cos A. TST (3) Suppose... | |
 | Victor Schlegel - Arithmetic - 1878 - 768 pages
...3) «nb = — -r— — ; 4) sm a sin a Aufgabe 3. — Gegeben bc«. Wenn man in der Formel 336 (a) cos a = cos b . cos c + sin b . sin c . cos a die Substitution macht: (b) cos a — cot b . co< y, so erhält man cos a = cos b (co* C + sin C .... | |
 | Johann Odstrčil - Quaternions - 1879 - 96 pages
...— cos a, so erhält man eine andere Form der Fundamentalgleichung der sphärischen Trigonometrie cos A + cos B cos C — sin B sin C cos a. 28. Nimmt man dagegen die Vectortheile, so hat man « sin A = y cos B sin C + /3 cos 6' sin $ + F/37... | |
 | Carl Friedrich Gauss, Friedrich Wilhelm Bessel - Astronomy - 1880 - 644 pages
...findet : tang ß2 + tang C* — 2 tang B tang C cos a = sec /?z + sec C2 — 2 sec B sec C cos A oder cos A = cos B cos C + sin B sin C cos a usw Hieraus leitete ich, dadurch dass ich aus diesen Gleichungen sin «, sin 6, sin c bestimmte, sin... | |
 | Alexander Ross Clarke - Geodesy - 1880 - 390 pages
...put T\ e2 cos2 <£ = i : then on equating these values of BC2, we get after a slight reduction, 0 = 2 (cos a — cos b cos c— sin b sin c cos A') where H= 4bccoaA'—3c2-b2 = —a2- 2 accost, K- 4bccosA'—3b*—c2 = -a2 — 2at>cos C. Now put for... | |
 | Geology - 1881 - 566 pages
...wir aus der spliärischen Trigonometrie die vier Grundgleichungen: sin_a_sinj> ' siifä ~ süT/T 2) cos a — cos b cos c = sin b sin c cos a. 3) cos a -+- cos ß cos f — sin ß sin y cos a. 4) ctg a sin b = cos b cos f -+- sin f ctg a. Aus... | |
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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. 
