Calendar: 1873-1874 Page 552

552 GENERAL LITERATURE AND SCIENCE and hence deduce that a- 2bc Show how to solve triangle in whicli are given the sides and the angle and show in what cases there are two solutions one or none If there are two solutions and cl c2 are the third sides of the two triangles the distance between the centres of their circum- scribing circles is sin Find expressions for the area of triangle and also for the radius of the circumscribing circle in terms of the sides If perpendiculars be drawn from the angular points of tri- angle Β to meet the opposite sides in DEF the radius of the circle circumscribing Ε is half the radius of the circle circumscribing ABC 10 Assuming De Moivre's theorem deduce formulae for the expansion of sin and cos in series of powers of and find the exponential values of sin and cos Reduce to the form β 11 Prove that tan -12 χ 4-- and deduce convenient series for calculating the value of π 12 Show that when η is even -l r-l cos 2x cos η cos 47 2t cos '2π η η jr 5jr 71r Show that sin sin sin sin 7- 16 16 16 16V2