 | Benjamin Williamson - 1873 - 406 pàgines
...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 - 1873 - 536 pàgines
...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... | |
 | Aaron Schuyler - 1875 - 284 pàgines
...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 pàgines
...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... | |
 | Henry Nathan Wheeler - 1876 - 218 pàgines
.... 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... | |
 | Karl Klein - 1876 - 504 pàgines
...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 .... | |
 | Harvard University - 1876 - 554 pàgines
...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,... | |
 | Benjamin Williamson - 1877 - 442 pàgines
...expression for the difference between the other sides, as far as terms of ihe second order in i. Here cos c = cos a cos b + sin a sin b cos C. Let 2 denote the difference in question ; ie c = a - 2 ; then cos a cos 2 + sin a sin 2 = cos « cos... | |
 | Johannes Frischauf - 1877 - 216 pàgines
...Dreieck C'AB ist C'A = b" = 2 Л - b, C'B — «" = 2 R - a, Winkel C' = C. Da a" < R, b" <R ist, so ist cos c = cos a" cos b" + sin a" sin b" cos C', cosc = cos(2Д — a)cos(2Л — b) + sin(2B — a)sin(2.ß — b)cosC, woraus wieder cos c = cos a... | |
 | Naturforschende Gesellschaft in Zürich - 1877 - 922 pàgines
...Proportion l Sin vers C Sin a . Sin b Sin vers c — Sin vers (a—b) eben, die eine Umgestaltung von Cos c = Cos a Cos b + Sin a Sin b Cos C ist So wurde 1587 I 29, 4y2h Abends im westlichen -Wimuthe 47° 0' die Holte der Venus 30° 46' erhalten,... | |
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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. 
