Calendar: 1866-1867 Page 471

GENERAL LITERATURE AND SCIENCE 47 column on pedestal 20 feet high subtends 45 to spectator be approaches 20 feet and finds the column subtends the same angle as before find the column's height Show that sin sin cos Β sin Β cos Find sin and cos Ζ in terms of sin and cos and deduce sine cosine and tangent of 18 10 If in triangle sin sin Β sin "C and a5 b3 c3 c2 the triangle is equilateral 11 Trace sin cos in value and algebraic sign through the quadrants being and its multiples 12 If be the three angles of triangle show that sin sin Β sin -1-i- -ϊ tan sin sin Β -f sm 13 Find the sine and cosine of 15 and 75 and show that sec 75 cosec 75 γ 14 Solve the equations sin2 sin 2Λ sin sin sin' sin3 15 If cos χ prove without assuming De Moivre's theorem that cos xe χ and ץ sin x6 -ך 16 Given 8563 7821 48 -24 find Λ and Β log 1-6384 2144199 cot 24 12103473497 log 78704039 42 tan 0066צ00 45 difi' for 10012655