 | Leonard Magruder Passano - 1918 - 176 pàgines
...of cosines : COB a = coab cos c + sin b sin c cos A, cos b— cos c cos a + sine sin a cos B, (37) cos c = cos a cos b + sin a sin b cos C, by means of which any spherical triangle may be solved. For example, given a = 60°, b = 70°, A =... | |
 | 1920 - 852 pàgines
...(14) cos a = cos b cos c + sin b sin c cos A , (15) cos 6 = cos c cos o + sin c sin a cos B, ( 16) cos c = cos a cos b + sin a sin b cos C. From these, by passing to the polar triangle (of equal generality with that of Fig. 13), one finds... | |
 | Asiatic Society (Kolkata, India) - 1920 - 656 pàgines
...summarised below there are then at least traces of the following rules of spherical trigonometry : — (i) cos c = cos a cos b + sin a sin b cos C (ii) sin A sin c = sin a sin C (Hi) cos A sin c = cos a cos b — sin a cos 6 cos C where A, B, C are... | |
 | 1920 - 898 pàgines
...triplet : (14) cos a = cos b cos c + sin b sin c cos A, (15) cosfr = cose cos a + sine sin a cos B. (16) cos c = cos a cos b + sin a sin b cos C. From these, by passing to the polar triangle (of equal generality with that of Fig. 13), one finds... | |
 | Robert William Chapman - 1922 - 272 pàgines
...formulae : — . cos A = — cos B cos 0 + sin B sin C cos a"| cos B = — cos C cos A + sin C sin A cos b >• . (4) cos C = — cos A cos B + sin A sin B cos c } Whilst the formulae (2) and (3) and (4) are extremely useful in all sorts of investigations into... | |
 | Thomas Vipond Barker - 1922 - 178 pàgines
...c that is wanted, and not A and B, in which case its value can be computed, either by the formula : cos c = cos a . cos b + sin a . sin b . cos C, or in two purely logarithmic stages by the following- pair of formulae : tan x = tan a . cos C ; cos... | |
 | Pauline Sperry - 1928 - 88 pàgines
...permutation of the letters gives two other forms of formula (2), cos b = cos c cos o + sin c sin a cos B, cos c = cos a cos b + sin a sin b cos C. What modifications of the proof are necessary for Figures 10 and n? Either the law of cosines for sides... | |
 | Robin Michael Green - 1985 - 540 pàgines
...Apply the cosine formula to triangle ABC (Fig. 1.5), obtaining cos b = cos a cos c + sin a sin c cos B, cos c — cos a cos b + sin a sin b cos C. Eliminate cos c from the first equation, and replace sin c by using the sine formula. The result is... | |
 | Nicholas P. Cheremisinoff, Louise Ferrante - 1989 - 224 pàgines
...of Cosines for Sides cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b + sin a sin b cos C Law of Tangents tan '/2(fl - C) _ tan '/2(¿> - c) tan '/2(5 + C) ~ tan lA(b + c) tan '/2(C - X) _... | |
 | Mark F.C. Ladd, Rex A. Palmer - 1994 - 616 pàgines
...sine and cosine rules in spherical triginometry, we have sin A _ sin B _ sin C sin a sin b sin c and cos c = cos a cos b — sin a sin b cos C (1.30) Thus, in the triangle dcr, cr = b = 35.27°, dcdr = B = 45°, dr = c, decr = C = 90°. Hence,... | |
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B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G. 
