| William Smyth - Navigation - 1855 - 234 pages
...tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of 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. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,... | |
| William Mitchell Gillespie - Surveying - 1855 - 436 pages
...to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every... | |
| Elias Loomis - Trigonometry - 1855 - 192 pages
...A+sin. B_sin. i(A+B) cos. i(A—B)_cos. i(A— B) _ sin. (A+B) ~sin.|(A+B) cos. i(A+B)~cos.i(A+B)' that is, The sum of the sines of two arcs is to the sine of their sum, as the cosine of half the difference of those arcs is to the cosine of half... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...(2.) In the same way it may be shown that THEOREM II. In any plane 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. By Theorem I., we have 5 : c : : sin.... | |
| Peter Nicholson - Cabinetwork - 1856 - 518 pages
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of... | |
| William Mitchell Gillespie - Surveying - 1856 - 478 pages
...to each other a* the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every... | |
| William Mitchell Gillespie - Surveying - 1857 - 538 pages
...to each other at the opposite sides. THEOREM II.— In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every... | |
| Elias Loomis - Trigonometry - 1859 - 218 pages
...A+sin. B—sin. ^(A+B) cos. |(AB)—tang. ~ ~ _ sin. A-sin. B~sin. £(AB) cos. (A+B)~tang. KA~B) ' that is, The sum of the sines of two arcs is to their...those arcs is to the tangent of half their difference. cos oof" .Dividing formula (3) by (4), and considering that -.— =s— ^ sin. xC R =- - (Art. 28),... | |
| Euclides - 1860 - 288 pages
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B... | |
| George Roberts Perkins - Geometry - 1860 - 472 pages
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : :... | |
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