| Cornell University - 1875 - 1012 pages
...sin'.r=:2cosa;r — 1 = I — 2sinV. 4. Prove that in any plane triangle the sum of cither two sides **is to their difference as the tangent of half the sum of** the opposite angles is to the tangent of hall' their difference. 5. Given two sides of a triangle equal... | |
| Aaron Schuyler - 1875 - 284 pages
...£(Л + ß) : tan £(Л — B). Hence, In any plane triangle, the sum of the sides inchuling an angle **is to their difference as the tangent of half the sum of** the other two angles is to the tangent of half their difference. We find from the proportion, the equation... | |
| William Hamilton Richards - 1875 - 216 pages
...from 180°, E + F = 180° 150° T — 29° 3'. and \ (E + F) = 14° 31' 30". The sum of the two sides **is to their difference, as the tangent of half the sum of** the angles at the base, to the tangent of half their difference. Ar. co. Log. (e + /) 3922'92 = 6'406347... | |
| Benjamin Greenleaf - 1876 - 204 pages
...<• ' sin Л -f- sin В _ cot|(X — B) . . * ' and by (14), that is, The sum of the sines of two **angles is to their difference as the tangent of half the sum of** the angles is to the tangent of half their difference, or as the cotangent of half their difference... | |
| Henry Nathan Wheeler - 1876 - 130 pages
...sides of any triangle are proportional to the sines of §72. The sum of any two sides of a triangle **is to their difference as the tangent of half the sum of** the opposite angles is to the tangent of half their difference . . 73 § 73. The square of any side... | |
| Henry Nathan Wheeler - 1876 - 254 pages
...sides of any triangle are proportional to the sines of { 72. The surn of any two sides of a triangle **is to their difference as the tangent of half the sum of** the opposite angles Is to the tangent of half their difference . . 78 § 73. The square of any side... | |
| Elias Loomis - 1877 - 458 pages
...|(A+B) cos. |(A— B)_tang. ~ "" sin. A— sin. B~sin. |(A— B) .cos. |(A+B)"~tang. i(A— B)' that is, **The sum of the sines of two arcs or angles is to their...difference as the tangent of half the sum of those arcs** is to the tangent of half their difference. Since the sides of a plane triangle arc as the sines of... | |
| 1878 - 710 pages
...TRIGONOMETRY. Scientific Clatt. 1. Demonstrate, that in any plane triangle, the sure of any two sides **is to their difference, as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. 2. Give the limiting values of the... | |
| Eugene Lamb Richards - 1878 - 134 pages
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO RIDES **is to their DIFFERENCE as the TANGENT of HALF the sum of** the OPPOSITE ANGLES 18 to the TANGENT of HALF their DIFFERENCE. Let A CB be any triangle. Then EC+CA... | |
| Michael McDermott - 1879 - 552 pages
...their contained Angle given to Find the other Side and Angles. 203. Rule. The sum of the two sides **is to their difference, as the tangent of half the sum of** the opposite angles is to the tangent of half their difference ; ¿ «., a -f Ъ : a — b : : tan.... | |
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