 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...  Plane and Spherical Trigonometry - Page 173by James Morford Taylor - 1905 - 234 pagesFull view - About this book
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...still equal to the sine of G. 7» 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 В C be any spherical triangle, 0 the... | |
 | Horatio Nelson Robinson - Navigation - 1878 - 564 pages
...gives COB. A CD _ cot. AC CO&.BCD ~ cot.BC Or, cot.J.tf : cot.BC = cos.ACD : cos.BCD. PROPOSITION VII. The cosine of any side of a spherical triangle is...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, and CD... | |
 | Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...would equal C (Ch. 16, VIII.). 111. In a right-angled spherical triangle, the cosine of the hypotenuse is equal to the product of the cosines of the other two sides. LetJ.JJC'be a triangle rightangled at B, and on the surface of a sphere whose centre is O, the vertex... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...cos a cos c + sin a sin c cos B, • • (4.) cos c = cos a cos b + sin a sin 6 cos C. • • (5.) That is, the cosine of any side of a spherical triangle is equal to the rectangle of the cosines of the two other sides, plus the rectangle of the sines of these sides into... | |
 | Elias Loomis - Trigonometry - 1886 - 436 pages
...5 + sin. a sin. b cos. C. (3) These equations express the following Theorem : The cosine of either side of a spherical triangle is equal to the product of the cosines of the two other sides plus the product of the sines of those sides into the cosine of their included angle.... | |
 | Webster Wells - Trigonometry - 1887 - 200 pages
...sin a _ sin b _ sin c sin A sin В sin C 156. In any spherical triangle, the cosine of either side is equal to the product of the cosines of the other two sides, plus the continued product of their sines and the cosine of their included angle. In the right triangle BCD,... | |
 | Thomas Marcus Blakslee - Trigonometry - 1888 - 56 pages
...sin6 sin A. . • . sin a : sin b = sin A : sin B. Law of Cosines. The cosine of any side of a (sph.) triangle is equal to the product of the cosines of the other two sides, plus the product of their sines hy the cosine of their included angle. Pythagorean Analogy: cosa = cosj» cos m, cosb =... | |
 | Henry Hunt Ludlow - Logarithms - 1891 - 322 pages
...у = сов or cos /Î + sin or sin /Î cos C. . . . (139) That is: Лиг eosine of any faec-angtt is equal to the product of the cosines of the other two face-angles, plus the product of their sines multiplied by the cosine of their included dihedral. 132.... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 202 pages
...still have sin DEG = sin B. 91. Law of Cosines. — In any spherical triangle, the cosine of each 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. Let ABC be a spherical triangle, O the centre... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...still have sin DEG = sin B. 191. Law of Cosines. — In any spherical triangle, the cosine of each 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. Let ABC be a spherical triangle, O the centre... | |
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