# Calendar: 1863-1864 Page 533

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GENERAL LITERATURE AND SCIENCE 533 cot cot cot cot 10 Find the area of regular polygon of η sides described about circle of given radius Hence deduce the area of tbe circle The area of regular polygon is J2 square yards find the length of side 11 Find all the values of χ in the equation sec χ sin2 χ -f- cos j2 jf sin sin β cos2 sin β sin cos2 β then sin sin β sin sin β 13 From vessel was observed another from the north sailing in direction parallel to its own In ρ hours its bearing was and in hours afterwards γ" from the North In what direction were the vessels sailing 14 The elevation of tower 100 feet high when due of an observer was 60 what will it be after he has walked due 400 feet given tan 13 53247166 tan 13 54247475 15 If Λα Bb Cc be perpendicular from on the sides of the triangle ABC and if from point Ο within the triangle Oav Obv Ocv be drawn at right angles to the sides then Ξ1 4- 4- 9h is Cc 16 Expand sin χ according to the powers of and thence show that tan 17 Find the roots of the equation x3 by trigone- metrical formulas

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