 | Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...an easy solution of the following problem. PROP. vir. (43.) Given the sines and cosines of two arcs, to find the sine and cosine of their sum and difference. Let AOB be the greater angle w, and BOC the lesser «/. Then AOC will be the sum "> + «/, or the difference... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...the fundamental formula of Plane Trigonometry, and nearly the whole science may be derived from it. Given the sines and cosines of two angles, to find the sine of their difference. By formula (a). sin. (d+/3) = sin. d cos. /3+ sin. /3 cos. 6. For d substitute... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...the fundamental formula of Plane Trigonometry, and nearly the whole science may be derived frotn it. Given the sines and cosines of two angles, to find the sine of their difference. By formula (a). sin. ($+/3) = sin. 6 cos./3+ sin. /3 cos. 1 For 6 substitute 180°... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...cos (540° ± A), tan A = ±tan (180°± A). ON FORMULAE INVOLVING MORE THAN ONE ANGLE. 19- Given (he sines and cosines of two angles, to find the sine and cosine of their sum or difference. NM PLANE TRIGONOMETflY. From any point P in OP draw PQ perpendicular to OQ, and from... | |
 | John Radford Young - Nautical astronomy - 1848 - 412 pages
...by M. Sarrus in the Annales des Mathematiques, tom. xi. Given the sines and cosines of two arcs or angles, to find the sine and cosine of their sum and difference. Let AM = a, and AN = a', be any two arcs of the circle, the radius being unity, then drawing the chord... | |
 | Harvey Goodwin - Mathematics - 1849 - 588 pages
...A = - cos (540° ± A), tan A = ± tan (180° ± A). ON FORMULA INVOLVING MORE THAN ONE ANGLE. 19. Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference. Let POQ, QOM be any two angles, which call A and D respectively. From any point P in... | |
 | London univ - 1852 - 358 pages
...and define the sine and cosine of an angle, tracing their variations through four right angles. 6. Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference. 7. Express the area of a triangle in terms of its sides. 8. How is fluid pressure estimated... | |
 | Thomas Kimber - Mathematics - 1865 - 302 pages
...first be multiplied by 3, the second by 4, and the third by 5, the sum of the products shall be 66. 6. Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference. 7. Express, in a form adapted to logarithmic computation, the area of a triangle, in... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...sin. A b sin. B b sin. B ' c sin. C ' c sin. C (ART. 6.) Investigation of General Formulas. PROBLEM I. Given the sines and cosines of two angles, to find the sine of their sum. Let ABC be a plane triangle (see the last figure) ; then, by equation 2, theorem 1 ,... | |
 | Henry Nathan Wheeler - Plane trigonometry - 1876 - 130 pages
...AND DIFFERENCE OF TWO ANGLES, AND FORMULAS DEDUCED FROM THEM. § 46. Given the sine and cosine of any two angles, to find the sine and cosine of their sum and of their difference. Let a and (3 denote the two angles, and let OP, o^ and FIG. 34. OR be so drawn... | |
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Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference. 