| Elias Loomis - Geometry - 1871 - 302 pages
...^(A+B) . sin. A-sin. B~sin. ^(AB) cos- ^(A+B)~tang. ^(AB) ' that is, The sum of the sines of two arcs **is to their difference, as the tangent of half the sum of** those arcs is to the tangent of half their difference. COS f*fvt Dividing formula (3) by (4), and considering... | |
| William Frothingham Bradbury - Geometry - 1872 - 268 pages
...BCD, being supplements of each other, have the same sine, and BD = a sin. BCD = a sin. C (41) B 102. **In any plane triangle, the sum of any two sides is...difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. Let ABC (Art. 103) be a plane triangle... | |
| Edward Olney - Geometry - 1872 - 566 pages
...horizontal parallax. PLANE TRIGONOMETRY. 86. Prop.— TJie sum of any two sides of a plane triangle **is to their difference, as the tangent of half the sum of the angles opposite** is to the tangent of half their difference. 1 >K\r. — Letting a and b represent any two sides of... | |
| Edward Olney - Geometry - 1872 - 472 pages
...horizontal parallax. PLANE TRIGONOMETRY. 80. Ргор.— The sum of any two sides of a plane triangle **is to their difference, as the tangent of half the sum of the angles opposite** is to the tangent of half their difference. ( DEM. — Letting a and b represent any two sides of a... | |
| Edward Olney - Trigonometry - 1872 - 216 pages
...horizontal parallax. PLANE TRIGONOMETRY. 86. Prop.— Tlie sum of any two sides of a plane triangle **is to their difference, as the tangent of half the sum of the angles opposite** is to the tangent of half their difference. DEM. — Letting a and b represent any two sides of a plane... | |
| Charles Davies - Geometry - 1872 - 464 pages
...have the following principle : In any plane triangle, the sum of the sides including either angle, **is to their difference, as the tangent of half the sum of the** two other angles, is to the tangent of half their difference. The half sum of the angles may be found... | |
| Boston (Mass.). School Committee - Boston (Mass.) - 1873 - 454 pages
...any plane triangle the sides are proportional to the sines of the opposite angles. III. Prove that **in any plane triangle the sum of any two sides is...their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. IV. In a triangle the side AB = 532. "... | |
| New York (State). Legislature. Assembly - Government publications - 1873 - 820 pages
...(CB); whence we have the principle. When two sides and their included angles are given : The sum of the **two sides is to their difference as the tangent of half the sum of the** other two angles is to. the tangent of half their difference. This young man also worked out a problem... | |
| Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1873 - 352 pages
...the other two sides. Prove it. 5. Prove that in a plain triangle the sum of two sides about 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 diff.rence. 6. One point is accessible and another... | |
| Aaron Schuyler - Measurement - 1873 - 520 pages
...tan \(A + B) : tan \(A — B). Hence, In any plane triangle, the sum of the sides including an angle **is to their difference as the tangent of half the sum of the** other tiuo angles is to the tangent of half their difference. We find from the proportion, the equation... | |
| |