Calendar: 1893-1894 Page 839

FACULTY OF SCIENCE CXV11 passes through the middle points of the six edges and find its equation 23 straight line moves parallel to the plane of xy and intersects the axis of ζ at height above the plane of xy pro- portional to the cosine of the angle which it makes with the axis of What is the equation of the surface generated 24 Prove that the two straight lines χ cos θ sin β sin θ cos θ lie wholly on the surface x2 y2 z2 ά b2 and interpret the meaning of the angle Θ Prove that the plane containing the two generators that pass through any point on the surface contains the tangent line to any plane section of the surface that passes through that point Cvtgonometn YEARS II Express the other principal Trigonometrical ratios in terms of the tangent If tan θ i5 verify arithmetically that sin30 sec cos30 cosectf sin cos cot tan Also prove that this is always true Establish formulae expressing cos 2A and cos in terms of cos and deduce therefrom that cos 6A 32 cos 6A 48 cos 18 cos 2A Explain the meaning of the notation sin-1 Why is it ambiguous State an obtuse value of sin-1 an acute value of tan and negative value of cos-1 Prove that sin-1 sin1 sin-1 £