 | Science - 1883 - 1552 pages
...erhält man schliesslich nach gehöriger Transformation und Einführung der Abkürzungen (14) i JV= sin a" sin b sin c' — sin a' sin b" sin c A = sin «' cos b" sin c — sin a" cos b sin c' B = sine' sin («"—a') C = sin a' sin (c' — r... | |
 | Royal Society (Great Britain) - Mathematics - 1885 - 496 pages
...6+sin a sin 6 cos C. From this equation may be deduced, as in Spherical Trigonometry, the relations sin A sin B sin C sin a sin b sin c Hence the geometry of any plane in elliptic space is the same as the geometry of a sphere in ordinary... | |
 | William John M'Clelland - 1885 - 182 pages
...Similarly, by letting fall a perpendicular DF on OB we get sin B sin a = —y=j = sin A sin b; hence sin A sin B sin C sin a sin b sin c' 33. Expressions for the sine, cosine, and tangent of half an angle of a triangle as functions of the... | |
 | Volkmar Hoffman - Mathematics - 1886 - 674 pages
...c) sin (6— a) sin a sin 6 sin a sin 6 . sin (6 — c) . gin(e — o) , sin (a — 6) sin (a — 6) sin a ' sin b ' sin c sin a sin b sin c (sinasm& — sincsm(a-\-b — c)) = — ~-~ .-- . . ^ / . . , . . / i \\ sin (a — 6) (cos (a —... | |
 | Henry Colthurst Godwin - 1894 - 384 pages
...Oblique-angled triangles. Fia. 100. Let ABC in Fig. 100 represent any oblique-angled spherical triangle; then sin A sin B sin C sin a sin b sin c ' .--, _ =tan _ sin . 8m cos c = cos a cos 6 + sin a sin 6 cos C; .... <1) A~B __ . A _ /sin (* —... | |
 | James Edward Oliver - Trigonometry - 1890 - 186 pages
...a, •••, s by sup. E, s — a by A — E, LAW OF SINES. THEOR. 8. In any spherical triangle ABC sin a: sin b : sin c = sin A : sin B : sin c. For, draw DC arc-ordinate of c as to AB, and letp = DC ; [fig. page 104 then •.• sinp = sin b sin... | |
 | James Edward Oliver - Trigonometry - 1891 - 180 pages
...sin B = sin 6 • sin A, .•. sin a : sin b = sin A : sin u. So sin b : sin c = sin B : sin c. .•. sin a : sin b : sin c = sin A : sin B : sin c. QED Translated into words, th. 8 is : /» any spherical triangle the sines of the sides are proportional... | |
 | George Albert Wentworth - Surveying - 1895 - 404 pages
...A >- [44] sin b sin C = sin c sin BJ These equations may also be written in the form of proportions sin a : sin b : sin c = sin A : sin B : sin C. That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite... | |
 | Great Britain. Civil Service Commission - Civil service - 1896 - 112 pages
...development of crystallographic theory which follows from this series. tve that in a spherical triangle sin A sin B sin C sin a sin b sin c ' Deduce the relation which connects the small variation of a side and the opposite angle. m 9. If... | |
 | Mathematics - 1896 - 754 pages
...ABC, A, B, C les angles opposés ; 2p — a + b + c) : cos a = cos b cos c -f- sin b sin c cos A ; (1) sin a sin b sin c sin A sin B sin C ' cot a sin I = cos b cos c -f- sin c cot A ; (3) cos A = — cos B cos C -j- sin B sin C cos a ; (4)... | |
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Oblique spherical triangles sin A sin B sin C sin a ~~ sin b sin c cos a = • cos b 
