 | Royal Astronomical Society - 1871 - 718 pages
...the geometrical proof would be more simple, I give the analytical one, as it may be useful. We have cos C = — cos A cos B + sin A sin B cos c, and thence — sinC<fC = (sin A cos B + cos A tin B co» e) d A + (sin B cos A + tin A cos B cos c)... | |
 | Edward Olney - 1872 - 562 pages
...= — cos B cos c + sin B sin c cosa ; ) (2) cos B = — cos A cos c + sin A sin C cos b ; \ B. (3) cos C = — cos A cos B + sin A sin B cos c. ) GENERAL FORMULA. we have a = 180° - A', ft = 180° — B', c = 180° - C', A = 180* - a', B = 180°... | |
 | 1872 - 412 pages
...the geometrical proof would be more simple, I give the analytical one, as it may be useful. We have cos C = — cos A cos B + sin A sin B cos c, 208 Prof. Cayley, on the Orbit xxxil. 5, and thence — tin C •." C = (sin A cos B + cos A sin B... | |
 | Aaron Schuyler - 1873 - 536 pages
...group, (1) cos a = cos b cos c -f- sin b sin c cos A. (2) cos b = cos a cos c + sin a sin c cos J3. (3) cos c = cos a cos b + sin a sin b cos C. 137. Proposition III. The co-sine of either angle of a spherical triangle is equal to the product of... | |
 | Benjamin Williamson - 1873 - 406 pages
...connecting the Variations of Three Sides and One Angle. — Differentiating the well-known relation cos c = cos a cos b + sin a sin b cos C, regarding a and b as constants, we get dc sin a sin b sin C dC sin c = sin a sin B. dc Again, the value... | |
 | Aaron Schuyler - 1875 - 284 pages
...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'. Changing the signs and omitting the accents, since the formulas are true for any triangle, we have... | |
 | Dublin city, univ - 1876 - 420 pages
...triangle prove the relation ra cos A + i cos B -fe cos C B a + b + e 3. In a spherical triangle prove the formula cos c = cos a cos b + sin a sin b cos C, and deduce the corresponding formula by aid of the polar triangle. 4. What do the preceding resslts... | |
 | Harvard University - 1876 - 554 pages
...angle which differs more from 90° than another angle is in the same quadrant as its opposite side. cos C + cos A cos B = sin A sin B cos c. 2. In the spherical oblique triangle MNO, given m, n, M; obtain, by Napier's and Bowditch's rules,... | |
 | Karl Klein - 1876 - 504 pages
...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. cos A 4- sin A . cotg B cotg c . sin b — cos b . cos A -t- sin A .... | |
 | Henry Nathan Wheeler - 1876 - 218 pages
.... cos a = cos b cos c + sin b sin c cos A, and similarly cos b = cos c cos a + sin c sin a cos B, ' cos c = cos a cos b + sin a sin b cos C. NOTE. What has been said about the measurement of straight lines in § 2, Plane Trig., will apply equally... | |
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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. 
