 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...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... | |
 | Daniel Alexander Murray - Spherical trigonometry - 1908 - 132 pages
...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... | |
 | Sir George Howard Darwin - Astronomy - 1908 - 540 pages
...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... | |
 | Robert Stawell Ball - Spherical astronomy - 1908 - 528 pages
...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 - Science - 1909 - 368 pages
...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 - Surveying - 1910 - 58 pages
...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 - Algebra - 1914 - 574 pages
...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... | |
 | Alfred Monroe Kenyon, Louis Ingold - Trigonometry - 1913 - 300 pages
...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... | |
 | Trinity College (Dublin, Ireland) - 1913 - 752 pages
...feet, and its vertical height is 5 feet: find its volume. 4. In a spherical triangle prove the formula cos c = cos a cos b + sin a sin b cos C. Ex. Given a = 68' 5', b = 73° 4', (7= 81° 10', find e. 5. Find the area of a field OA BCI)E which... | |
 | Herbert Bell - Spherical trigonometry - 1915 - 82 pages
...cos B cos C + sin B sin C cos a\ Similarly | cos B = - cos C cos A + sin C sin A cos 6V . . (7) and I cos C = - cos A cos B + sin A sin B cos c! These three equations together with group (5) complete the case (3.1). § 22. Fundamental Formulae.—We... | |
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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. 
