 | Mathematics - 1835 - 684 pages
...180° - 6 6 > 90° A > 90° a > 180° - 6 The first is evident on inspection of r, i sin- A sm. В = sin. 6 sin. a as no sine can be > 1. The four last...shown to follow, from the formula cos. a — cos. ¿>. cos. с cos. A = ; — ; — г sm. 6 sin. с which, since sin. 6 and sin. с are positive (5)... | |
 | Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...limiting form of the proposed formula will be a relation in Plane Trigonometry. For example, in Art. 106, from the formula , cos a — cos b cos c cos A = - . — ; — r sin b sin c we deduce now suppose r to become infinite; then ultimately and this is the expression for... | |
| |
Let a, 6, and A, be the data in case 5. Then in all cases sin. 6 sin. A must be < or = sin. a. And when b < 90° A > 90° «... must be . . . > b b > 90°... 