 | Francis Nichols - Plane trigonometry - 1811 - 162 pages
...is, in any spherical triangle the cosine of half the sum of any two sides is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. 78. Remark. From this proposition and cor. we obtain half the sum S, and... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...is to the sine of half their difference, as the tangent of half the side to they are both adjacent is to the tangent of half the difference of the other two sides ; that is, in the spherical triangle ABC (figs. 4. and 5.), sin. J (A + C) : sin. i (A — C)... | |
 | Charles William Hackley - Trigonometry - 1838 - 336 pages
...(9) That is, the cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The second may be repeated in a similar manner, chang. ing cosine into... | |
 | Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...triangle. 91. Theorem. The cosine of half the sum of two sides of a triangle is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles, or in (figs. 32 and 33), соз4(а^с) : cos?4(a— c)=:cotan. \B : tang.... | |
 | Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...triangle. 91. Theorem. The cosine of half the sum of two sides of a triangle is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles, or in (figs. 32 and 33), cos.£(a— c) : cos.|(a— c)=cotan.£J5 : tang.... | |
 | Charles William Hackley - Trigonometry - 1851 - 524 pages
.... That is, the cosine of half the sum of two sides of a spherical triangle it to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The second may be repeated in a similar manner, changing cosine into sine... | |
 | Charles William Hackley - Trigonometry - 1851 - 526 pages
.... That is, the cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half ike sum of the other two angles. The second may be repeated in a similar manner, changing cosine into... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...sum of any two sides of a spherical triangle is to the sine of the half difference of the same sides, as the cotangent of half the included angle is to the tangent of the half difference of the other two angles. The half sum, and the half difference of two angles of... | |
 | Benjamin Peirce - Trigonometry - 1861 - 398 pages
.../ 90. Theorem. The sine of half the sum of two sides of a spherical triangle is to the sine of half their difference as the cotangent of half the included...difference of the other two angles ; that is, in ABC (fig. 32 or 33), sin. J (a -fc) : sin. \ (a — c) = cotan. JB : tang. J (A — C). (369) Proof. This... | |
 | Benjamin Peirce - Plane trigonometry - 1861 - 394 pages
...55". 90. Theorem. The sine of half the sum of two sides of a spherical triangle is to the sine of half their difference as the cotangent of half the included...the difference of the other two angles ; that is, in ABO (fig. 32 or 33), sin. \ (a -fc) : sin. ¿ (a — c) = cotan. £ В : tang. \ (A — C). (369) Proof.... | |
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