 ... 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 136by Robert Woodhouse - 1822 - 264 pagesFull view - About this book
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...sin. (s—a) sin. s sin. (s—b) sin. 5 sin. (5— c) ) (C'".) § 58. ^7b eospress the sine of a side of a spherical triangle, in terms of the sines and cosines of the angles. By (B) § 56, we have cos A+ cos. B cos. 0 cos. a ~ . — =5-- — ~- ; consequently, _cos.A+cos.... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...one of the fundamental relations of Spherical Trigonometry. § 56. To express the cosine of a sida of a spherical triangle, in terms of the sines and cosines of the angles. Let A, B, C, a, b, c, bo the angles and sides of a spherical triangle, and A', B', C', a',... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...previously determined from the equation tan. 0=tan. b cos. A. PROBLEM IV. To express the cosine of a side of a spherical triangle in terms of the sines and cosines of the angles. Solution. Let A, B, C, a, b, c be the angles and sides of a spherical triangle ; A', B', C',... | |
 | Great Britain. Education Department. Department of Science and Art - 1886 - 640 pages
...less than three right angles. (30). 54. Prove the fundamental formula for expressing the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides. Does the proof establish the truth. of the formula in all cases ? and, if not, in what way does it... | |
 | 1902 - 762 pages
...SURVEYING. -PABT II. SECOND PAPER. The Board of Examiners. 1. Deduce an expression for the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides. 2. Deduce an expression for the area of a spherical triangle. 3. Compute the discharging capacity of... | |
 | University of Cambridge - Universities and colleges - 1810 - 324 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—y", y being the distance from the center... | |
 | Physics - 1825 - 500 pages
...depends, and which being transformed gives the well-known equation for expressing the cosine of a side of a spherical triangle in terms of the sines and cosines of the opposite angle and the other sides. This equation, which Delambre and other late writers make the foundation... | |
 | Cambridge Philosophical Society - Philosophy - 1827 - 522 pages
...by the angles xy, xz, yz, and the angle opposite to xy is 77. Hence, the above is the expression for the cosine of the angle of a spherical triangle in terms of the sides. ffV - -A .-X Y fig-3 '/ rA", ' \\ XII. On the Figure assumed by a Fluid Homogeneous Mass, ivliose... | |
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