Calendar: 1898-1899 Page 746

cxiv FACULTY OF SCIENCE cos Β have the same sign if and opposite signs if What is meant by 7r Prove that π lies between and An arc of 12 feet on circle of 10 feet diameter subtends an angle approximately 137 3035 find the value of π as accurately as these data permit State the extreme limits between which sin sec and tan can vary Trace graphically the changes in the value of sin ץ cos as changes from to 360 and shew that the resulting graph is sine curve whose greatest ordinate is twice the greatest ordinate of the curve representing sin Prove geometrically when and Β are obtuse angles that cos cos cos Β sin sin Also being acute that cos 2Λ -tan2J tanM Prove that tan2A sin2 cos cos2 2A cos 2A cos2 2A cot2 sin2 2A The sine of an angle is 13 find the tangent of the angle and the tangents of double and of half the angle explaining clearly the reason for any ambiguity that may occur Draw an illustrative diagram Shew that the sides of any plane triangle are propor- tional to the sines of the opposite angles Find the tangent of the base angle of an isosceles triangle in which two of the medians contain right angle YEARS II Solve the triangle having given the sides 374 58 462 91 589-34 and find its area Two vertical columns standing on horizontal plain are ρ such that the angles of elevation of the tops of each as seen from the bottom of the other are α β prove that the cosines of the angles each subtends from the top of the other are as sec sin tan β sec β sin β tan