Calendar: 1871-1872 Page 581

THE SCHOOL 581 Divide an angle geometrically into two parts whose tangent shall be in given ratio Prove geometrically the formula for tan in terms of tan Deduce the value of sin 18 from Euclid Book IV Prop 10 Prove the formula μ -I- cos cov" cos λΑ sin3 sin 3A ------ tan' β lau' β -------- cos 2a cos 2p 7r 27r 37r 41r sin sin sin sin 5' 16 tan -f tan 79 If Β 180 'an cos cos cos cos cos cos Λ If θ be less than show that sin θ Θ tan β are in order of magnitude Find the limit of their ratio when θ approaches zero Find also the limit of cos cos- cos- cos when the integer η is indefinitely increased Investigate formula for transforming the logarithm of number from one system of logarithms to another Show that log tan Θ log tan cosec 26 2cosec 26 cot 26 K1 approximately when is small When does the principle of proportional parts fail to determine an angle from the log tangent If and the angle be given show when there will be two triangles Find in terms of β and the distance between the centres of the circles described about the triangles 10 Find the radii of the inscribed and escribed circles of given triangle