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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... "
An Elementary Treatise on Plane & Spherical Trigonometry: With Their ... - Page 172
by Benjamin Peirce - 1845 - 449 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...reducing to entire terms, we have, cos a — sin b sin c cos A = cos 6 cos c ; and by transposing, cos a — cos b cos c + sin b sin c cos A. A similar equation may be deduced for the cosine of either of the other sides : hence, cos a = cos...
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Elements de géométrie et de trigonométrie, á l'usage des candidats aux ...

M. E. Gouré - Geometry - 1852 - 644 pages
...résolution des triangles sphériques quelconques. Le principe du n° 75 conduit aux deux égalités cos a — cos b cos c = sin b sin c cos A , cos b — cos a cos c = sin a sin c cos B. En divisant la seconde par la première, et en ayant sin...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...this case must contain a, b, c, and A. The f1rst of equations (1) contains these four quantities : cos a = cos b cos c + sin b sin c cos A. If A = 90° cos A = 0 ; hence, cos a = cos b cos c • that is, radius, which is 1, into the sine of...
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Des Méthodes en géométrie

Paul Serret - 1855 - 168 pages
...ne doivent pas être retenues, et qu'il suffit d'apprendre à les lire rapidement sur la figure, i. cos a — cos b cos c + sin b sin c cos A. On a, dans le triangle rectiligno nbr, Remplaçant chaque ligne par sa valeur, réduisant au même...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - Trigonometry - 1856 - 272 pages
...-b, b' = 180° - В C' = 180° - e, c' = 180° - C and applying the first equation of (4) to A'B'C', cos a' = cos b' cos c' + sin b' sin c' cos A' or by PI. Trig. (64), — cos A = (— cos B) (— cos C) + sin 5 sin C (— cos a) — cos A = cos 5...
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The American Journal of Education, Volume 2

Henry Barnard - Education - 1856 - 768 pages
...a sin. i — cot. A gin. C = cos. i cos. C, and by the consideration of the supplementary triangle cos. A = — cos. B cos. C + sin. B sin. C cos. a. Right-angled triangles. — Formulas cos. a — cos. Jcos. c; sin. i= sin. a sin. B; tang. e= tang,...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...c' cos A1 : substituting for a', b', c' and A', their values from the polar triangle, we have, — cos A = cos B cos C — sin B sin C cos a ; and changing the signs of the terms, we obtain, cos A = sin B sin C cos a — cos B cos C. Similar...
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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - Logarithms - 1858 - 292 pages
...two angles one of which is included by the sides; for instance between a, b, A, C. In the equation cos a = cos b cos c + sin b sin c cos A, substituting for cos c and sin c their values cos c -- cos a cos b + sin a sin b cos C, sin C sm c...
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Annalen der Physik und Chemie, Volume 2; Volume 108; Volume 184

Chemistry - 1859 - 698 pages
...berechnen, wenn man nur für eine aufser z auch x und x' gemessen hat. Winkel WMN durch A, so hat man: cos a — cos b cos c + sin b sin c cos A cos a' — cos b cos c — sin b sin c cos A oder Bezeichnet man den Bogen MN durch b und den (3) ,...
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Leçons de geométrie analytique: comprenant la trigonométrie rectiligne et ...

Lefébure de Fourcy (M., Louis Etienne) - Geometry, Analytic - 1859 - 578 pages
...cos b cos c En chassant le dénominateur, et (ransposant cos « dans le premier membre , il vient [1] cos a = cos b cos c + sin b sin c cos A. Telle est la formule fondamentale de la trigonométrie sphérique. 94. Dans la figure les côtés b...
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