 | William Augustus Norton - Astronomy - 1839 - 530 pages
...74. cos c = cos a cos b -j- sin a sin b cos C cos c = cos (a — 6) — 2 sin a sin b sin3^ C cos C = sin A sin B cos c — cos A cos B sin a cos c = sin c cos a cos B + sin b cos C sin a cot c = cos a cos B + sin B cot C sin a cos B = sin c... | |
 | Thomas Keith - 1839 - 498 pages
...by equations (1) and (2) of art (244), sin (A + B+c)-sin (A+B) ' cos c+cos rad _(sin A . cos B+COS A . sin B) . cos c ~" ' " " " (cos A . cos B — sin A . sin B) . sin c "~ ..... rada ...... " I 3 ' cos c~sin (A+B) • si" c cos rad _{cos A . cos B — sin A... | |
 | John Hymers - Astronomy - 1840 - 386 pages
...SPK = cos /, and applying these values and the fundamental formulas of spherical Trigonometry, viz. cos c = cos a cos b + sin a sin b cos C, cot .4 sin C = cot a sin 6 — cos C cos 6, sin a sin B = sin .4 sin b, (where «, 6, c, A, S, C, represent... | |
 | Mathematics - 1841 - 722 pages
...Vorzeichen, so seien dieselben zuerst beide positiv. Dann ist offenbar, wenn sin a sin b positiv ist, cos a cos b + sin a sin b cos C~^ cos a cos b + sin a sin l>, di cos a cos ¿ + sin a sin b cos 6'^ cos (0 — 6), woraus das zu Beweisende folgt. Wenn aber... | |
 | Mathematics - 1841 - 552 pages
...seien dieselben zuerst beide positiv. Dann ist offenbar, wenn sin a sin b positiv ist, cos u cos b -H- sin a sin b cos C ^, cos a cos b •+• sin a sin f>, di cos 0 cos Ä-r-sin « sin £ cos C^cos (a — 6), woraus das zu Beweisende folgt. Wenn aber... | |
 | Nathan Scholfield - 1845 - 894 pages
...these angles, and the third angle of the triangle. By (a) \ve have, cos. a — cos. 6 cos. c cos. A = And, cos. C = sin. b sin. c cos. c — cos. a cos....sin. b cos. c = cos. a cos. b + sin. a sin. b cos. C (1.) . . . (2.) Substituting this value of cos. c in Equation (1.) : cos. a — cos. a cos.' b —... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...cos. a — cos. b cos. c . . • • " • • • •* (•*•) cos. A = And, cos. C = sin. b sin. c cos. c — cos. a cos. b sin. a sin. b .'. cos. c — cos. a cos. i + sin. a sin. b cos. C - - - (2.) Substituting this value of cos. c in Equation (1.)... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...angles. For instance, sin (A + B + C) = sin (A + B) cos C + cos (A + B) sin C = (sin A cos B + cos A sin B) cos C + (cos A cos B — sin A sin B) sin C Similarly we may express cos ( A + B + C), tan (A + B + C), &c., in terms of the trigonometrical... | |
 | Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...: thus, (1) cos a = cos b cos c + sin b sin c cos A (2) cos b = cos a cos c + sin a sin c cos B (8) cos c = cos a cos b + sin a sin b cos C. and as the three equations at the end of the last article together contain all the six parts of a triangle,... | |
 | Franz Brünnow - Astronomy - 1851 - 634 pages
...Fälle umfasst: cos a = cos b cos c + sin b sin c cos A cos b = cos o cos c + sin o sin c cos B {1) cos c = cos a cos b + sin a sin b cos C sin a sm U — sin b sin . l EID a sin C' — sin c sin .1 (3) sin 6 sin C = sin c sin /•' sin o... | |
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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. 
