Calendar: 1896-1897 Page 698

CV111 FACULTY OF SCIENCE Find the other angles of triangle having given Β 45 1725-3 1013-92 cot 22 3010-3827757 log 7-1138 8521017 tan 32 597971938 log 24376237 7392 tan 32 697974745 log 27393 4376396 YEAR III 13 Observations are made from ship of two stations known to be in the same meridian The angle they subtend is when the first is due β when the second is due Find the direction of the ship's course 14 If be the radius of the circumcircle and the radius of the incircle of plane triangle ABC prove that 4R sin sin sin If the triangle be spherical triangle pro re that π ci Β tan tan cos cos cos sin sin sm 15 Find all the values of Prove that π cos sin -1 16 If find the sum to infinity of cos2 m2 cos2 2a m3 cos2 3a 17 Prove that cosh sinh cosh sinh Hence expand coshm in series of hyperbolic cosines of multiples of integral Calatht£ YEAR III may substitute amy of the folloioing for questions 13-17 18 State and establish the method of integration bv sub- ο stitution Apply the method to sins χ cos χ dx dx 19 Explain the method of integrating φ χ where and φ χ are two rational integral algebraic functions of ---- and hence shew that χ έ Λ ----to inf 7r3 log