... sun in the meridian. The arches being supposed semi-circular, it is required to find the curve terminating that part of the surface of the water which is illuminated by the sun's rays passing through any arch. 7- It is required to express the cosine... A treatise on plane and spherical trigonometry - Page 130by Robert Woodhouse - 1822Full view - About this book
| 1804 - 130 pages
...illuminated by the sun's rays passing through any arch. 7- It is required to express the cosine of an **angle of a spherical triangle in terms of the sines and cosines of the sides.** 8. If a body revolves in any curve whose equation is ap—yn, y being the. distance from the centre... | |
| Sydney Smith, Lord Francis Jeffrey Jeffrey, Macvey Napier, Henry Reeve, William Empson, Arthur Ralph Douglas Elliot (Hon.), Sir George Cornewall Lewis, Harold Cox - 1810
...the solution of which he derives all the rules, are these : To express the cosine and the sine of an **angle of a spherical triangle in terms of the sines and cosines of the sides.** There is a double advantage in this manner of proceeding -, the whole process is rendered analytical,... | |
| Francis Nichols - Plane trigonometry - 1811 - 128 pages
...: : ' . sine a sine c A similar formula may be readily obtained for the cosines of any of the sides **of a spherical triangle in terms of the sines and cosines of the** three angles. For since any spherical triangle, whose three angles are A, B, C, and three opposite... | |
| Mathematics - 1821 - 425 pages
...illuminated by the sun's rays passing through any arch. . 7. It is required to express the cosine of an **angle of a spherical triangle in terms of the sines and cosines of the sides.** • .- • :v, 8. If a body revolves in any curve whose equation is ap = yn, y being the distance from... | |
| Nathan Scholfield - Conic sections - 1845 - 232 pages
...the sine of the sum of two angles is to plane trigonometry. CHAPTER I. 1. To express the cosine of an **angle of a spherical triangle in terms of the sines and cosines of the sides. Let** ABC be a spherical triangle, O the centre of the sphere. Let the angles of the triangles be denoted... | |
| 1845
...c sin. a sin. c cos. e — cos. a cos. ft sin. a sin. ft cos. a 2. To express the cosine of a side **of a spherical triangle, in terms of the sines and cosines of the** angles. Let A, B, C, a, ft, c, be the angles and sides of a spherical triangle ; A', B', C', a', ft',... | |
| Nathan Scholfield - Geometry - 1845 - 232 pages
...a)sin.(s — &) tan.— =V/ ; : — -. r — 2 v sin. s sin. (s — c) 4. To express the sine of a side **of a spherical triangle in terms of the sines and cosines of the** angles. By (/3) we have, cos. a= cos. A+cos.Bcos. C sin. B sin. C cos. A+cos. B cos. C+sin. B sin.... | |
| Conic sections - 1845
.... — : sin. a sin. c cos. c — cos. a cos. 6 cos. C= sn. a sn. 2. Tb express the cosine of a side **of a spherical triangle, in terms of the sines and cosines of the** angles. Let A, B, C, a, b, c, be the angles and sides of a spherical triangle ; A', B', C', a', b',... | |
| Thomas Grainger Hall - Trigonometry - 1848 - 168 pages
...INVESTIGATION OF FORMULAS FOR THE COSINE AND SINE OF THE ANGLES AND SIDES OF A SPHERICAL TRIANGLE. 17. To find **the cosine of the angle of a spherical triangle in terms of the** cosines and sines of the sides. Let 0 be the intersection of the three planes A OB, А ОС, БОС.... | |
| James Hann - 1849
...called an isosceles triangle, &c., as in Plane Trigonometry. 10. To determine the sines and cosines **of a spherical triangle in terms of the sines and cosines of the sides. Let** O be the eentre of the sphere on which the triangle ABС is situated, draw the radii OA, OB, OС; from... | |
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