 In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of...  Elements of Trigonometry, Plane and Spherical - Pàgina 51per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pàginesVisualització completa - Sobre aquest llibre
 | William Kent - 1902 - 1224 pàgines
...formulœ enable us to transform a sum or difference into a product. The sum of the sines of two angles is to their difference as the tangent of half the sum of those angles is to the tangent of half their difference. sin A + sin В 2 sin ЩА + B) cos WA - B)... | |
 | Preston Albert Lambert - 1905 - 120 pàgines
...B) Since a and b are any two sides of the triangle, in words 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 the difference of these angles. The formula a -H1 _ tan £(A... | |
 | James Morford Taylor - 1905 - 256 pàgines
...one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of half their difference. From the law of sines, we have By... | |
 | International Correspondence Schools - 1906 - 634 pàgines
...formulas are derived in Appendix II. 20. Principle of Tangents. — 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. That is (Fig. 6), a + d _ ta a - b ~ tan... | |
 | 1906 - 230 pàgines
...formulas are derived in Appendix ll. 20. Principle of Tangents. — 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. That is (Fig. 6), ab tan i (A - B) The... | |
 | Fletcher Durell - 1910 - 348 pàgines
...sin C' sn . sin В 107 TRIGONOMETRY 75. Law of Tangents in a triangle. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the angles opposite the given sides is to the tangent of half the difference of these angles. In a triangle ABC (Figs.... | |
 | Fletcher Durell - 1911 - 336 pàgines
...sin A sin B 107 sin C' TRIGONOMETRY 75. Law of Tangents in a triangle. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the angles opposite the given sides is to the tangent of half the difference of these angles. In a triangle ABC (Figs.... | |
 | Robert Édouard Moritz - 1913 - 562 pàgines
...a-6~tan|^-B)' 6-c~tan|(BC)' c+a tang (ü + Л) c- a tan 5 (С - Л) Formulas (7) embody the Law of tangents: In any triangle, the sum of two sides is to their...the tangent of half the sum of the angles opposite is to the tangent of half their difference. The formulas (6), which we shall have occasion to use hereafter,... | |
 | Charles Sumner Slichter - 1914 - 516 pàgines
...follows that: b + c _ tan KB + C) _ b - c ~ tan i(B - C) (t)> _ _ _ ca~tani(CA) (l)) Expressed in words: In any triangle, the sum of two sides is to their...the tangent of half the sum of the angles opposite is to the tangent of half of their difference. GEOMETR1CAL PBOOF: From any vertex of the triangle as... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - 1914 - 308 pàgines
...solution by logarithms the following theorem is needed: TANGENT THEOREM. In any triangle the sum 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. „ „ a sin a: f . ,, Proof. T = - —... | |
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