# Calendar: 1889-1890 Page 758

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112 ENGINEERING DEPARTMENT 12 From point distant from the centre of circle of radius perpendiculars are drawn to the sides of regular polygon of η sides inscribed in the circle Express the sum of the squares of their lengths 13 State and prove De Moivre's Theorem and apply it to express the six sixth roots of unity 14 Prove that θ2 Θ cos θ --h ------- &c and write down the general term of this series How many seconds are there in the largest acute angle the cosine of which may be taken to be to places of decimals Any of the following questions may he substituted for any of 15 Simplify the preceding Η of of 31-1 11 of 3& 16 Shew how to divide £278 15s 6c amongst J9 and so that A's share iTs and £9s C's 17 Express in powers of prime factors 750 2880 and 10800 and thence find their and their 18 Find the present worth of £532 75 Id due years months hence simple interest being reckoned at per cent 19 Find the cube root of 82881856 20 Multiply 2976548293 by 18Ό46353798 so as to be right to places of decimal fractions Conic cttonS anU integral Calculus Prove that the equations 2x 3y and 5x 6j taken separately determine two straight lines and taken together determine one point Find the tangent of the angle between the lines and also the coordinates of the point Find the locus of point which moves so that the square of its distance from fixed point varies as its distance from fixed straight line

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