Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b... Academic Trigonometry: Plane and Spherical - Page 25by Thomas Marcus Blakslee - 1888 - 35 pagesFull view - About this book
| Daniel Cresswell - Geometry - 1816 - 352 pages
...complemental triangle. PROP. I. (230.) Theorem. The cosine of any one of the sides, of a spherical **triangle, is equal to the product of the cosines of the other two sides,** together with the continued product of the sines of those two sides, and the cosine of the angle contained... | |
| Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...triangles. In the form of a theorem it may be stated thus : The cosine of one of the sides of a spherical **triangle^ is equal to the product of the cosines of the other two sides,** increased by the product of their sines multiplied into the cosine of the included angle. There are... | |
| William Chauvenet - 1852 - 268 pages
...the various positions of the lines of the diagram. 5. In a spherical triangle, the cosine of any side **is equal to the product of the cosines of the other two sides, plus the** continued product of the sines of those sides and the cosine of the included angle. Let the plane B'A'С',... | |
| Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...cot.BC Or, cot. AC : cot.BC = cos. ACD : cos.BCD. PROPOSITION VII. The cosine of any side of a spherical **triangle, is equal to the product of the cosines of the other two sides, plus the product of** the sines of those sides multiplied by the cosine of the included angle. Let ABC be a spherical triangle,... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...the sine of C. (147) (148) (149) TRIGONOMETRY. 149. In any spherical triangle, the cosine of any side **is equal to the product of the cosines of the other two sides, plus the product of** the sines of those two sides into the cosine of their included angle. Let A BC be any spherical triangle,... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...of B1 Ö D is still equal to the sine of G. 149. In any spherical triangle, the cosine of any side **is equal to the product of the cosines of the other two sides, plus the product of** the sines of those two sides into the cosine of their included angle. Let ABC be any spherical triangle,... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...«till equal to the sine of C. 7* TRIUONOMETRY. 1 49. In any spherical triangle, the cosine of any side **is equal to the product of the cosines of the other two sides, plus the product of** the sines of those two sides into the cosine of their included angle. Let ABC be any spherical triangle,... | |
| Benjamin Greenleaf - 1867 - 188 pages
...In like manner, by means of (153), sinJB = ^°3^. (197) cos p ^ 161. T^e cosine of the hypothenuse **is equal to the product of the cosines of the other two sides.** By means of (152) we have cos A = cos p cos b -\- sin p sin b cos C, which, by making O = 90°, becomes... | |
| Eli Todd Tappan - Geometry - 1868 - 444 pages
...Trigonometry in Space. THREE 8IDE8 AND AN ANGLE. 878. Theorem. — The cos)ne of any side of a spherical **triangle is equal to the product of the cosines of the other two sides,** increased by the product of the sines of those sides and the cosine of their included angle. 315 Let... | |
| Edward Olney - Trigonometry - 1885 - 222 pages
...thought sufficient for the general student] 143- Prop- — In a Spherical Triangle the cosine of any side **is equal to the product of the cosines of the other two sides, plus the product of** the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b cos c... | |
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