 A = tan a/sin b . . (4) and the derived formula : — sin a sin b _ sin c sin A sin B sin C ' ' The " supplemental formulas " corresponding to these are given (as a cheap luxury) in the supplementary exercise, but "Napier's analogies...  The Teaching of Algebra (including Trigonometry) - 454. lappuseautors: Sir Thomas Percy Nunn, Thomas Percy Nunn - 1919 - 616 lapasPilnskats - Par šo grāmatu
 | Adrien Marie Legendre - 1832 - 482 lapas
...proposition , sin A : sin a : : sin B : sin b : : sin C : sin c ; ce qui donne la double équation : sin A sin B _ sin C sin a sin b sin c ' LXXVI. Dans tout triangle sphérique le cosinus d'un angle est égal au quarré du rayon multiplié... | |
 | Simon Newcomb - 1882 - 372 lapas
...the angles are all supposed to be less than 180°, the positive signs are to be taken. Hence sin A _ sin B _ sin C sin a ~ sin b ' ~ sin c ' the reciprocal of the relations (2). 1O1. Polar triangles. Def. When two triangles are so related . that... | |
 | 1894 - 576 lapas
...read off the scales as easily as the cosine, having got a, b, c, and C, and using the formulae sin a _ sin b _ sin c sin A sin B sin C ' the angles A and B can be found by drawing lines through 90— a, 90 — 6, parallel to the line joining... | |
 | Josiah Willard Gibbs, Edwin Bidwell Wilson - 1901 - 470 lapas
...sin B = sin b sin C sin a sin C = sin c sin A are obtained. These may be written in a single line. sin A sin B _ sin C sin a sin b sin c The formulae of Plane Trigonometry are even more easy to obtain. If ABC be a triangle, the sum of the sides... | |
 | Thomas Ulvan Taylor, Charles Puryear - 1902 - 242 lapas
...Similarly, and sin c sin C sin a _ sin A sin ft sin B sin & sin B sin c sin C From these equations, we have sin a sin b _ sin c sin A sin B sin C 92. Law of Cosines. In a spherical triangle the cosine of any side equals the product of the cosines... | |
 | Thomas Percy Nunn, Sir Thomas Percy Nunn - 1914 - 760 lapas
...tan a/sin b . (4) and the derived formula : — sin a sin b sin c sin A "" sin B ~ sin C " • \ J The " supplemental formulas " corresponding to these...other complications introduced in order to obtain formulas adapted to logarithmic computation are entirely beyond the requirements of the ordinary student... | |
 | Leonard Magruder Passano - 1918 - 176 lapas
...righthand member would be identical with that written above. Therefore, obviously, we have sin A _ sin B _ sin C sin a sin b sin c the law of sines which was to be proved. CHAPTER IX THE SOLUTION OF RIGHT SPHERICAL TRIANGLES 73. Special... | |
 | Leonard Magruder Passano - 1918 - 198 lapas
...righthand member would be identical with that written above. Therefore, obviously, we have sin A _ sin B _ sin C sin a sin b sin c ' the law of sines which was to be proved. CHAPTER IX THE SOLUTION OF RIGHT SPHERICAL TRIANGLES 73. Special... | |
 | Sir Robert William Chapman - 1919 - 266 lapas
...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 b sin c (b) One side of a triangle is expressed in terms of the two other sides, and the angle included between... | |
 | Bruno Pattan - 1993 - 420 lapas
...cos A o The Law of Cosines for angles: cos A = - cos B cos C + sin B sin C cos a o The Law of Sines: sin A . sin B _ sin C sin a sin b sin c o Napier's Rules of Circular Parts (for right spherical triangle ABC): complement A = 90° - A B =... | |
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