Calendar: 1875-1876 Page 577

GENERAL LITERATURE AND SCIENCE 573 Apply Euclid IT 10 to determine tbe sine and cosine of one- fifth of right angle Prove that Α ύ Α Vl tan2Λ tan -- and -- ------ cos tan Why has the latter formula two values and the former hut one How is the sign to he determined in any particular case Prove that when θ is indefinitely diminished sin Θ tan Θ are all equal Find the ultimate value of tan 20 2tan0 when θ is indefinitely diminished If Β be multiple of 180 then will cot Β cot cot cot -f cot cot Β If Β 2m π or ur then will sin cos sin Β cos sin cos sin sin Β sin -f- cos cos cos but if Λ 20 π or 2ottt then will sin cos vi sin Λ cos sin -J- cos sin sin sin cos cos Β cos 7-1 Shew how to solve triangle in which are given the sides β and the angle and determine in what cases there are two solutions one or none If there be two triangles having the given parts and if cv e3 be their third sides the distance between the centres of their cir- cumscribing circles sin Shew that the product of the diameter of the circle circum scribing triangle by the sum of the perpendiculars on the