Calendar: 1880-1881 Page 642

642 GENERAL LITERATURE AND SCIENCE Assuming1 De Moivre's theorem find the values of cos0 J- sind being in its lowest terms 11 Expand sin in series of simple sines 12 Shew how to resolve χ into factors 13 In any spherical triangle cot cota coti cot tanc -------- C0t C0ttf COS fCOSZ 14 The arc of great circle bisecting the sides AB AC οί opherical triangle cuts BC produced at shew that jr cos Qsm -י s1n -ο- sm 15 Find the sum of η terms of the series sina sinCa β sin -f- man walks on plane in such manner that when he nas passed over distance in straight line he always changes his path through the same angle in the same direction Shew that when he has done this η times his distance from his starting point is and that this distance makes an ang with his first path