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" ... sin(a + b + c). Again (a) represents the coarse ROM, and bands b and c are two controls of the fine-tuned ROMs so that a < 90°, b < 90 • 2~a and c < 90 • 2~(a + 6). This is shown in Fig. 7-7. Sunderland showed that the trigonometric identity... "
Key to System of practical mathematics. 2 pt. No.xvii - Σελίδα 15
των Scottish school-book assoc - 1845
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A Treatise on Plane and Spherical Trigonometry

Robert Woodhouse - 1819 - 264 σελίδες
...+ C) as sin. (/4 + B) cos. C + cos. (^ + B) . sin. C = sin. A cos. B cos. C+ cos. A sin. B cos. C + cos, A cos. B sin. C — sin. A sin. B sin. C. Subtract [2] from [4], and cos. (A — B) - cos. (A + B) =* 2 sin. Л . sin. В [*]. If we substitute...

Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - 1833 - 264 σελίδες
...will be 0, so that the first of these equations gives sin. A cos. B cos. C + cos. A sin. B cos. C + cos. A cos. B sin. C = sin. A sin. B sin. C ; dividing both sides of this equation by cos. A cos. B cos. C, we have sin. A . sin. B . sin. C sin. A sin. B sin. C "~ nna...

Proceedings of the American Association for the Advancement of Science

American Association for the Advancement of Science - 1892
...cos B sin C sin A — cos C sin A sin B, and sin a ' ' ' = cos -B cos C sin A + cos C cos A sin B + cos A cos B sin C — sin A sin B sin C, which are identical with the formula? in plane trigonometry. If further A = B = C, a?A = cos3 A —...

Principles of the Algebra of Physics

Alexander Macfarlane - 1894 - 53 σελίδες
...sin C—cosB sin C sin A — cos C sin A sin B, and sin a = cos s cos O sin A + cosC cos A sin B + cos A cos B sin C — sin A sin B sin C, which are identical with the formulae in plane trigonometry. If further A = B = C, a 3A = cos 3 A —...

Plane Trigonometry, for Colleges and Secondary Schools

Daniel Alexander Murray - 1899 - 206 σελίδες
...B + C = 90°. (3) EXERCISES. 1. Show that sin(.4 + B + C) = sin A cos B cos C + cos A sin B cos C + cos A cos B sin C — sin A sin B sin C. If A + B + C = 180°, the first member is zero. Division of the second member by cos A cos B cos C...

Mathesis: recueil mathématique à l'usage des écoles spéciales ..., Τόμοι 22-23

1902
...conséquent Rt2co3Aco8BsinC(l -f- 2 ain* C) " ' ' ' ~ (1 + 2 sin1 A) (f+Tsîn"» ¥) ("f+^27inrC) ' Or, 2 cos A cos B sin C = sin A sin B sin C, 22 cos A cos B sin' C = 22 cos A cos B sin C — 22 cos A cos B sin C cos* C =» 2 sin A sin B sin...

Plane [and Spherical] Trigonometry for Colleges and Secondary Schools

Daniel Alexander Murray - 1908
...B + C = 90°. (3) EXERCISES. 1. Show that sm(.4 + B + C) = sin A cos B cos C + cos A sin B cos C + cos A cos B sin C — sin A sin B sin C. If .4 + B + C = 180°, the first member is zero. Division of the second member by cos A cos B cos C...

Digital Frequency Synthesis Demystified: DDS and Fractional-N PLLs

Bar-Giora Goldberg - 1999 - 336 σελίδες
...Sunderland showed that the trigonometric identity can be written as sin(a + b + c) = sin(a + 6) cos c + cos a cos b sin c - sin a sin b sin c (7-10) which is approximately sin(a + 6) + cos a sin c (7-11) This suggests that the addressing of...
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Leerboek Der Meetkunde

P Molenbroek - 1896
...(a-\-b) -\- c \ = sin (djb) cos c -f- cos (a-\-b) sin o = sin a cos b cos c -)- cos a sin b cos c -j- cos a cos b sin c — sin a sin b sin c , of sin (a -f- b -f- c) = sin a cos b cos c -)- sin b cos a cos c -)- sin c cos a cos b — sin a...
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