Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b... Plane and Spherical Trigonometry - Pągina 173per James Morford Taylor - 1905 - 234 pąginesVisualització completa - Sobre aquest llibre
| Alfred Hix Welsh - 1894 - 228 pągines
...the sine of its supplement. SPHERICAL. THEOREM II. In any spherical triangle, the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of their sines into the cosine of their included angle. Let ABC be a spherical triangle, and 0 the centre... | |
| Webster Wells - 1896 - 308 pągines
...sin С sin с apd - sn_ = sma ( sin С sin с 152. In any spherical triangle, the cosine of any side is equal to the product of the cosines of the other two sides, plus the continued product of their sines and the cosine of their included angle. In the right triangle BCD,... | |
| George William Jones - 1896 - 216 pągines
...upon these laws. THE LAW OF COSINES. THEOR. 5. In a triedral angle : (a) The cosine of a face angle is equal to the product of the cosines of the other two face angles less the product of their sines by the cosine of the opposite diedral: ie cos a = cos b... | |
| 1897 - 726 pągines
...proportional to the sines of the opposite angles. That is, sin a : sin 5= sin A : sin B The cosine of any side equal to the product of the cosines of the other two sides plus the product of their sines and the cosine of the included angle. That is, cos a=cos b cos c+sin 5 sin c cos A TO-,... | |
| 1900 - 804 pągines
...proportional to the sines of the opposite angles. That is, sin a: sin b = sin A : sin B The cosine of any side equal to the product of the cosines of the other two sides plus the product of their sines and the cosine of the included angle. That is, cos a = cos I cos e+sin I sin c cos A The... | |
| Pitt Durfee - 1900 - 340 pągines
...three ratios proj FE/FE, FE/FD, FD/OD, which can be interpreted. (b) The cosine of a diedral tingle is equal to the product of the cosines of the other two diedrals less the product of their sines by the cosine of the opposite face angle : ie co ft a = cos... | |
| Thomas Ulvan Taylor, Charles Puryear - 1902 - 248 pągines
...c sin A sin ii sin C [11] 92. Law of Cosines. In a spherical triangle the cosine of any side equals the product of the cosines of the other two sides plus the product of their sines and the cosine of their included angle, or, in symbols, taking the side a of the triangle... | |
| Joseph Claudel - 1906 - 758 pągines
...GENERAL FORMULAS 1078. Formula containing the three sides and an angle. Theorem. The cosine of any side a is equal to the product of the cosines of the other two sides, increased by the product of the sines of these two sides multiplied by the cosine of their included... | |
| William Charles Brenke - 1910 - 376 pągines
...sinbcos.4. Hence (2) cos a = cos Ь cos с + sin & sin с cos A. That is, the cosine of any side equals the product of the cosines of the other two sides plus the product of their sines by the cosine of their included angle. Exercise. Discuss the case where D falls on AB produced.... | |
| Alfred Monroe Kenyon, Louis Ingold - 1913 - 184 pągines
...OQ OR OQ OR or, since OP/ OR = cos c, PR/ OR = sin c, I. cos a = cos 6 cos c + sin 6 sin c cos A . The cosine of any side of a spherical triangle is...the other two sides plus the product of the sines of those two sides into the cosine of their included angle. Compare this with the law of cosines for plane... | |
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