 | Daniel Alexander Murray - 1908 - 358 pàgines
...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 - 368 pàgines
...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 pàgines
...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... | |
 | Trinity College (Dublin, Ireland) - 1913 - 752 pàgines
...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... | |
 | Sir Thomas Percy Nunn - 1914 - 574 pàgines
...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 - 1913 - 300 pàgines
...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... | |
 | Herbert Bell - 1915 - 82 pàgines
...Formulae.—If in the equation cos a = cos b cos c + sin b sin c cos A we substitute for cos c and sin c from cos c = cos a cos b + sin a sin b cos C and . . _ . . . sin c = sin U sin a/sin A we obtain . , . „ . . _. cot a si n b = cos b cos C + cot... | |
 | 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 =... | |
 | 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... | |
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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. 
