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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

A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872
...- AO = cos (180° - B1) cos (180° - C7) + sin (180° - B') sin (180° — C') cos (180" - a'), or, cos A' = — cos B' cos C' + sin B' sin C' cos a', since cos (180° — A*) = — cos A', etc. ; and sin (180° — B1) = sin B', etc. Finally, dropping...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 455 pages
...value La (2), we have, (20 and now substituting these values of OE, OZ>, and QP, in (1), we h'ave, cos a — cos b cos c + sin b sin c cos A • (3.) Jj the same way, we may deduce, cos b = cos a cos c + sin a sin c cos B • ' (4.) • cos...

Catalogue - Harvard University

Harvard University - 1873
...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',...

Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1873 - 490 pages
...— c'. Substituting these values in the formulas of the preceding article and reducing, we have — cos A'— cos B' cos C" — sin B' sin C" cos a'. — cos B' = cos A' cos 0" — sin A' sin C' cos b'. — cos C" = cos A' cos B' — sin A' sin B' cos...

Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 455 pages
...= sin b sin c cos A ; (2.) and now substituting these values of OE, OL, and QP, in ( 1 ), we have, cos a = cos b cos c + sin b sin c cos A • (3.) la the same way, we may deduce, cos b = cos a cos c + sin a sin c cos B • • (4.) cos c...

The Analyst, Volumes 9-10

Electronic journals - 1882
...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...

Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 184 pages
...C=Ш°—c'. Substituting these values in the formulas of the preceding article and reducing, we have — cos A'—~ cos B' cos C' — sin B' sin C" cos a'. — cos. B'= cos A' cos C"— sin A' sin C' cos b'. — cos C' = cos A' cos B' — sin A' sin B' cos...

Theorie der goniometrischen und der longimetrischen Quaternionen: zugleich ...

K. W. Unverzagt - Quaternions - 1876 - 312 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...