 | William Anthony Granville - Logarithms - 1909 - 322 pages
...diameter of inscribed circle. 8 = 180°— diameter of circumscribed circle. Law of sines, p. 207. sin a sin b sin c sin A sin B sin C sin a sin b sin c sin # sin ß sin y Law of cosines for the sides, p. 209. (12) cos a = cos b cos c... | |
 | 1910 - 322 pages
...tan l i- tan" e * e+a a+b 4 T^ MAiiti « t • *(h) Prove, if A, B, C be the angles of a triangle, (sin A - sin B + sin C) (sin A + sin B - sin C) ^ = 4 *m 2 — ; r- sin B gin C. xL ANNUAL EXAMINATION. PURE MATHEMATICS. PAPER b —ALGEBRA. Examiner:... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 330 pages
...spherical triangle the sines of the sides are proportional to the sines of the opposite angles. That is, sin a : sin b: sin c = sin A : sin B: sin C. (39) From equations (37) we have, cos A. = . Á cos a —• cos b cos c Whence sin b sin c 1 - cos... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 488 pages
...spherical triangle the sines of the sides are proportional to the sines of the opposite angles. That is, sin a : sin b : sin c = sin A : sin B: sin C. (39) From equations (37) we have, cos A — cos a ~ cos b oos c sin b sin c Whence 1 - COS 2 A=lsin... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 198 pages
...spherical triangle the sines of the sides are proportional to the sines of the opposite angles. That is, sin a : sin b : sin c = sin A : sin B: sin C. (39) From equations (37) we have, < cos a — cos b cos c cos A = - . sin b sin c Whence 1 _ cos 2... | |
 | Bernard Carra de Vaux - Civilization, Islamic - 1921 - 414 pages
...proportionnalité des sinus des angles à ceux des côtés (Chap. V) : —— = —-— = ——- ; Sin A Sin B Sin C Sin a Sin b Sin c et à ce sujet il écrit ce paragraphe qui est d'un intérêt capital pour l'histoire de cette science.... | |
 | Marshall Henry Haddock - Geology, Economic - 1926 - 358 pages
...expression to which sin B , sin C sin b sin c -—- and —— are also equal, hence the Rule of Sines, te sin A sin B sin C) sin a sin b sin c \ (iv) Equation between two sides and two angles all lying together (A, b, C, a).—By (68) (cos c)... | |
 | David E. Smith - Mathematics - 1958 - 756 pages
...seriously studied by itself until the Arabs began to consider it in the roth century. The Theorem of Sines, sin a — sin b — sin c sin A — sin B — sin C' and the Theorem of Cosines of Sides, cos a = cos b cos c + sin b sin c cos A, may have been known to... | |
 | Natural history - 1921 - 68 pages
...Formel. Nach den vorhergehenden Formeln ist für « = ¡i = "/ daher bei Vernachlässigung von a 2 sin A. sin B. sin C sin A* . sin B*. sin C* = 1 « Í2 b V sin^l. sinZÌ. sin C sin A* . sin B*. sin C" Die die Vergleichung kleiner geodätischer... | |
 | Nicholas P. Cheremisinoff, Louise Ferrante - Mathematics - 1989 - 224 pages
...SPHERICAL TRIGONOMETRY FORMULAS AND DEFINITIONS FOR OBLIQUE SPHERICAL TRIANGLES (Figure A27) Law of Sines sin a sin b sin c sin A sin B sin C C >\ a Figure A27. Spherical triangle. where a, b, c represent the sides of any spherical triangle... | |
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Oblique spherical triangles sin A sin B sin C sin a ~~ sin b sin c cos a = • cos b 
