...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...

...sin b cos C. These formulas embody the Law of Cosines: The cosine of any side of a spherical triangle is equal to the product of the cosines of the other two sides plus the continued product of the sines of these two sides and the cosine of the included angle. Fig. 32. Fig. 33(b) Second Proof....

...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 equal to the product of the cosines of the other two sides plus the product of the sines of those two sides into the cosine of their included angle. Compare this with...

...opposite angles. Example. — In Fig. 2, sin A : sin a : : sin С : sin c. 2. 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. Example. — In Fig. 2, cos n = cos...

...be as readily proved if D does not fall between A and B. 122. Cosine theorem (Law of cosines). — In any spherical triangle, the cosine of any side...the product of the cosines of the other two sides, increased by the product of the sines of these sides times the cosine of their included angle. Proof....

...sm С Hence (2) cos a = cos 6 cos с + sin ft sin с cos .4. 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...

...a the side is ir/2. The important trigonometric relation in a spherical triangle is as follows: I. The cosine of any side is equal to the product of the cosines of the two other sides plus the continued product of the sines of these sides and the cosine of the included...