Calendar: 1886-1887 Page 682

684 GENERAL LITERATURE AND SCIENCE tanl cot jPa Λ Δ raTbTc rar& r&rc rcra What are the exponential values of sin θ and cos θ Expand θ in series ascending by powers of tan Θ an prove that 4- --- Prove that in spherical triangle cos cos cos ב cos cosi cos cos and cos0 sin sin £ sin sin and deduce the equivalent relations in plane trigonometry Give Napier's rules for the solution of right-angle spherical triangles and write down the ten equations con necting the sides and angles taken three at time If ABC is spherical triangle right-angled at and CI an arc drawn perpendicular to AB prove that CI sin1 tan tani Prove that the area of the triangle the coordinates whose angular points are x2y2 8י Find the area of the triangle formed by the three straigh lines 3x 4y ha by 110 70 Find the angle between the straight lines representee by the equation ax1 by1 and determine when the angle between them is 2a and they are equally inclined to the straight line χ 10 Find the polar equation to circle and to the tangent at any point of it the pole being at the centre of the circle TP TQ are two fixed tangents to circle whose centre is and any third tangent meets them in and prove that the angle BOS is always of the same magnitude for all positions of the variable tangent