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" But a' = 180° - A, b' = 180° - ß, c' = 180° - C. and A' = 180° - a. Therefore, — cos A = (— cos B)(— cos C) + sin B sin C(— cos a... "
An Elementary Treatise on Plane & Spherical Trigonometry: With Their ... - Page 182
by Benjamin Peirce - 1845 - 449 pages
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A Complete Course of Pure Mathematics, Volume 2

Louis-Benjamin Francœur - Mathematics - 1830 - 506 pages
...property of the supplemental triangle, change, in equ. (3), a into 180 — A, &c. ; and we shall have — cos A = cos В cos С — sin В sin С cos a. ..(5) To eliminate 6 from the equ. (3), first put for sine its value sin B sin a = : — -j — : let...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...from 0,„. sin. a sin. o sin. с We have then cos. A + cos. В cos. С = cos. a sin. В sin C, or — cos. A — cos. В cos. С — sin. В sin. С cos. a. For cos. A write its equal, — cos. (я- — A), and for sin. В its equal, sin. (я- — В), and...
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A Treatise on Trigonometry, and on Trigonometrical Tables and Logarithms ...

John Hymers - Logarithms - 1841 - 244 pages
...then QOP - B, 90° - (7, are the adjacent parts, and b, c, the opposite parts ; and the formula;, t cos A = - cos В cos С + sin В sin С cos a, cos a = cos 6 cos с + sin b sin с cos Д , since Л = 90°, and therefore cos.¿ = 0, sin A = l,...
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A Course of Mathematics: In Two Volumes. Composed for the Use of ..., Volume 2

Charles Hutton - Mathematics - 1843 - 570 pages
...cos В cos G, from eq. (4). Performing similar operations by means of^3 andp3, we shall readily get cos A = — cos В cos С + sin В sin С cos a -j cos В = — cos С cos A + sin С sin A cos 6 [• (5.) § cos С = — cos A cos В + sin A sin...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...— B, and 180° — C, and the included 180° — a; so that the polar triangle might be solved by 56. Corollary. If formula (307) is applied to the...section, it becomes by PI. Trig. §61, — cos. A = cos. B cos. C — sin. B sin. C cos. a, or cos. A = — cos. B cos. C-\- sin. Bsin. C cos. a. (317) 57....
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The Elements of Spherical Trigonometry

James Hann - Spherical trigonometry - 1849 - 84 pages
...between ABС and a, which, applied to the three angles successively, •will give the three equations cos A = — • cos В cos С + sin В sin С cos a (11) cos В = — cos A cos С + sin A sin С cos Ъ (12) cos С = — cos A cos В + sin A sin В...
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The Elements of Plane Trigonometry

James Hann - Plane trigonometry - 1854 - 140 pages
...cos A cos Б cos C= 1, cos Л = — cos (B + C) = — cos В cos С + sin В sin C, cos* A =• — cos A cos В cos С + sin В sin С cos A, cos2 В = — cos A cos В cos С + sin A sin С cos B, cos' A+ cos' В = — 2 cos A cos В cos С...
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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - Logarithms - 1858 - 292 pages
...part, then 90" — B, 90*— (7, are the adjacent parts, and b, c, the opposite parts ; and the formula cos A — — cos В cos С + sin В sin С cos a, cos a = cos Ъ cos с + sin Ъ sin с cos ^4, since A = 90° and therefore cos A = 0, sin Л = 1, become...
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Leçons sur la théorie des fonctions circulaires et la trigonométrie

Ignace Louis A. Le Cointe - Trigonometrical functions - 1858 - 420 pages
...obtenir l'une quelconque des trois relations, par exemple la première, il suffit d'observer que l'on a cos A -+- cos В cos С = sin В sin С cos a et i — tang3 tos ar= a tang'd'où l'on tire ta cos A 4- cos(B 4- C) tang! - = - — A4_cos(B_C) '...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1861 - 394 pages
...or, by (98) and (99), — cos. A = ( — cos. B] ( — cos. C) -f- sin. В sin. С ( — cos. a), or cos. A := — cos. В cos. С -(- sin. В sin. С cos. a ; and this equation, which may be applied to either of the three angles of a spherical triangle, is...
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