Calendar: 1873-1874 Page 614

614 THE SCHOOL than times the sum of its digits and if the order of the digits be reversed the number so formed is greater by 11 than times the sum of its digits find the number 16 If prove that and tliat 3ו d' rf Crigonomctrp Explain the three methods of measuring angles by degrees grades and circular measure and find the relations between the three measures of an angle The angles of triangle are in harmonic progression and the number of grades in the least the circular measure of the greatest 40 7r determine the angles Define the sine and the tangent of an angle and prove the relations- sin Λ sin 180 sin 90 cos and sin Α Γ tan2 tan Prove by geometrical constructions the formulae- sin sin cos Β -f cos sin smA sin sin Β c0i Having given sin Λ -1 and vmB n' find tan Find an expression for all the angles which have given sine Solve the simultaneous equations 2sin θ 2φ sin 26 3φ V3