...of triangles more accurate and convenient. Let us first take the fundamental equation (1) of Chapter I., cos a = cos b cos c ~\- sin b sin c cos A. We may express this in the form cos a = cos b cos c -|- sin b sin c — sin b sin o (1 — cos A) \...

...auch x und x gemessen hat. Bezeichnet man den Bogen MN durch b und den Winkel durch A, so hat man: [ cos a = cos b cos c + sin b sin c cos A \ cos «'= cos b cos c — sin b sin r cos A oder l a' + a a' — o <4> l . , . i . «+a. .-. sin o...

...b; cos a sin b — cos A sin C = cos 6 cos C, et par la considération du triangle supplémentaire, cos A = — cos B cos C + sin B sin C cos a. Formules relatives aux triangles rectangles. cos a = cos b cos c ; sin b = siu a sin B ; tang c = tang...

...findet : tang B2 + tang C2 — 2 tang /, tang C cos a = sec B2 + scc C2 — 2 sec R scc C cos A oder cos A = cos B cos C -\- sin B sin C cos a usw Hieraus leitete ich , dadurch dass ich aus diesen Gleichungen sin a, sin b, sin e bestimmte, sin...

...(uniting the three sides and one angle of a spherical triangle) which has no equivalent in Ptolemy: cos a = cos b cos c — sin b sin c cos A A further advance was made with Abu'1-Wafa', and he was probably the first to demonstrate the sine...

...tirer d'affaire en toutes circonstances, sans le secours d'imprimés qui risquent de faire défaut cos a = cos b cos c + sin b sin c cos A et : sin a sin b sin A sin B sin C Dans le triangle de position ces formules donnent : cos z = sin...

...for the sides is cos a = cos 6 cos c + sin 6 sin c cos A, while the law of cosines for the angles is cos A = - cos B cos C + sin B sin C cos a. There are two more formulae in each case obtained by simultaneous cyclical permutation of a, 6, c and...

...triangles are given by sin A sin B sin С .... —. = — — г = — : (25) sin a sin b sin c and cos a = cos b cos c + sin b sin c cos A (26) The point vertically above the observer is called his zenith and is denoted by Z. Thus OZ gives...

...(n-ß)i, <T2 = (ny)i. Hence, (3) takes the form sin a sin b sin c sin a sin ß sin y ' and (6) yields cos a = cos b cos c + sin b sin c cos a , and the analogues for cos b and cos c, cos a = — cos ß cos y + sin ß sin y cos a , and the analogues...

...triangle T**. The "law of cosines " for triangles in each of the three geometries of constant curvature is cos a = cos b cos c + sin b sin c cos a (K* > 0), a* = b* + c2 - 2bc cos a (K* = 0), cosh a = cosh 6 cosh c — sinh b sinh c cos a (K* < 0)....