 | Simon Newcomb - 1906 - 580 Seiten
...included angle C. r• • sin c sin A = sin a sin C, sin c cos A = cos a sin b ~ sin a cos b cos C, -. cos c = cos a cos b + sin a sin b cos C. If we compute k and K from k sin K=s\na cos 0, kcosK=cosa, then sin c cos A = k sin (b - K), cos c... | |
 | Daniel Alexander Murray - 1906 - 466 Seiten
...sin c cos A. (2) Similarly, or by taking the sides in turn, cos b = cos c cos a + sm c SMI 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... | |
 | Joseph Claudel - 1906 - 758 Seiten
...quantities a + b and a — b substituted in (1) or (2) give C. C may also be calculated directly. Thus, cos C = — cos A cos B + sin A sin B cos c, or cos C = — cos A (cos 5 — sin B tan B cos c). Let tan B cos c = cot 9, then cos C = — cos A... | |
 | Sir George Howard Darwin - 1908 - 540 Seiten
...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 - 132 Seiten
...sine cos A. (2) Similarly, or by taking the sides in turn, cos 6 = 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... | |
 | Daniel Alexander Murray - 1908 - 358 Seiten
...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... | |
 | Robert Stawell Ball - 1908 - 528 Seiten
...two adjacent angles are given then we require two new formulae (4) and (5) to be associated with (3) cos C = — cos A cos B + sin A sin B cos c (4), sin Ccosa= cos A sinfi + sin A cos B cos c (5), sin C sin a— sin A sine (3). respectively by... | |
 | Francis Rolt-Wheeler - 1909 - 368 Seiten
...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 - 58 Seiten
...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... | |
 | Sir Thomas Percy Nunn - 1914 - 574 Seiten
...position of P in fig. 72, and, in accordance with the argument of §§ 1, 2 of this exercise, we have that cos c = cos a cos b + sin a sin b cos C. But if the card were shifted so that A or B became the point of contact, it would follow that the angle... | |
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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. 
