 | John Bonnycastle - Trigonometry - 1818 - 488 pages
..._, . sin b sin a sin cini But since - — = - — = - — , we shall have sin B sin A sin c' Sin c (sin A + sin B) = sin c (sin a + sin 6) Sin c (sin A— sin B) = sin c (sin a— sin b) Which two equations, when divided by the preceding Sin A... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 pages
...Now if c and c be changed into B and b, or into A and a, the quantity M will not at all be altered. sin A sin B sin c sin a sin 6 sin c' . sin A sin a and hence also = — — r, &c (3). sm B sin b ^ ' This result shows that in every spherical... | |
 | Charles William Hackley - Trigonometry - 1851 - 524 pages
...to form the following equations, which are easily deduced from the fundamental formulas : — sin c (sin A ± sin B) = sin c (sin a ± sin 6)* sin c (cos A ± cos B) = (1 ^ cos c) sin (a ± &)t (1 ± cos c) sin (A ± B) = sin c (cos 4 Jt cos a)t which,... | |
 | A. Boset - Geometry, Analytic - 1881 - 730 pages
...(s — a) sin (s — 6) sin (s — c). XII. 1 — cps* a — coss 6 — cos8 c — 2 cos a cos 6 cos c = — 4 cos s cos (s — a) cos (s — b) cos (s — c). XIII. i -f- cos* a — cos* 6 — cos4 c -+- 2 cos a sin 6 sin c = 4 sin s sin (s — a) cos (s —... | |
 | Chemistry - 1897 - 598 pages
...= cos a cos b = cot A cot B A, B, C denote angles , a, b, c, opposite sides, _~*V^r_— «• and 2 sin A sin B sin C sin a sin 6 sin c cos A — — cos B cos C -\- sin B sin Ccos a cos a _ cos i'1 cos <- -j- sin /' sin c cos ^4 sin -... | |
 | Joseph William Mellor - Chemistry, Physical and theoretical - 1902 - 620 pages
...= OB = OA, CD . . CE OC ' " ~~ OC' CE Similarly, sin B . sin a = QQ = sin A . sin b ; and finally, sin A sin B sin C sin a ~ sin 6 ~ sin c ' ' As an exercise, show that this result is true for any spherical triangle. Note the formal resemblance... | |
 | Herbert Bell - Spherical trigonometry - 1915 - 82 pages
...representatives of the standard formulae for the three different cases— Sine Formula. Case (2.2). sin A sin B sin C , sin a sin 6 sin c Cosine Formula. Case (3.1). cos a = cos b cos c + sin b sin c cos AI . _. cosA=-cosBcosC + sinBsinCcosa... | |
 | Leonard Magruder Passano - Trigonometry - 1918 - 176 pages
...solution of Case 1. If a check is desired in the solution the law of sines may be so used. Thus, since sin A sin B sin C sin a sin 6 sin c ' it follows that log sin A — log sin a = log sin B — log sin b = log sin C — log sin c. It must... | |
 | Sir Robert William Chapman - Astronomy - 1919 - 270 pages
...relations : — (a) The sines of the angles are proportional to the sines of the opposite sides : — sin A — sin B — sin C sin a sin 6 sin c (b) One side of a triangle is expressed in terms of the two other sides, and the angle included between... | |
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C denote angles , a, b, c, opposite sides, _~*V^r_— «• and 2 sin A sin B sin C sin a sin 6 sin c... 