 | Sir George Howard Darwin, Sir Francis Darwin, Ernest William Brown - 1908 - 516 pągines
...sin b + cos a cos b cos C = sin a sin b + cos c cos C — sin a sin b cos2 C = sin a sin b sin* C + cos c (— cos A cos B + sin A sin B cos c) = sin A sin B sin' c + sin A sin B cos2 c — cos A cos B cos c = sin i sinj — cos i cosj cos N Substituting... | |
 | Daniel Alexander Murray - 1908
...sine cos A. (2) Similarly, or by taking the sides in turn, cos b = cos c cos a + sin c sin a cos B, cos c = cos a cos b + sin a sin b cos C. In words : In a spherical triangle the cosine of any side is equal to the product of the cosines of... | |
 | Francis Rolt-Wheeler - 1909
...general case of the universal law which is expressed in its simplest form by the Pythagorean Theorem : cos c = cos a cos b + sin a sin b cos C If the radius of the sphere is allowed to become great •without limit — that is, the spherical... | |
 | Joseph Baker Davis, Howard B. Merrick - 1910 - 47 pągines
...group below. cos a = cos b cos c + sin b sin c cos A. (2) cos b — cos c cos a -\- sin c sin a cos B. cos c = cos a cos b -\- sin a sin b cos C. HF = OH sin b. HT = HD cos b. DE = PE cos C. DE = HF — HT. sin a cos C = sin b cos c — cos b sin... | |
 | Alfred Monroe Kenyon, Louis Ingold - 1913 - 132 pągines
...Example 2. Given c = 40° 16', C = 52° 30', a = 47° 44'. To find 6 apply the law of cosines to side c. cos c = cos a cos b + sin a sin b cos C. .76304 = .67258 cos 6 + .74002 sin 6(.60876) .45047 sin 6 + .67258 cos b = .76304 Placing A(sin 6 cos... | |
 | Leonard Magruder Passano - 1918 - 141 pągines
...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
...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... | |
 | 1920
...(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... | |
 | Robin M. Green, Robin Michael Green - 1985 - 520 pągines
...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 - 200 pągines
...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(æ> - c) tan '/2(5 + C) ~ tan lA(b + c) tan '/2(C - X) _... | |
| |
A. {cos a = cos b cos c + sin b sin c cos A. cos b = cos a cos c + sin a sin c cos B. cos c = cos a cos b + sin a sin b cos C. 
