Calendar: 1880-1881 Page 639

GENERAL LITERATURE AND SCIENCE 639 12 If the whole number of persons born in any month is Tyth and the number of persons who die nr th of the whole population at the beginning of the month in how many months will the population double itself Given log 30103 log 4771213 log 845098 13 The angles of triangle are in Arithmetical Progression and the greatest is times the least express the angles in degrees grades and circular measure 14 Determine the values of the trigonometrical ratios for angles of 30 and 45 15 Compare the trigonometrical ratios of an angle and its supplement 16 Find an expression for all the angles that have given sine and write down the general value of Θ when sine θ 17 Give geometrical proofs for the expansions of sin cos tan 18 Solve the equations sin20 cos0 sin costf tan30 tan and show that in the last θ will not be real unless sin be less than 19 Prove that in any triangle cosA cosZ cosC sini sinC sin2A sin2i -f sin2 2cosAcosBcosC bcosB ccosC acos 20 Show how to solve triangle when two sides are given and an angle opposite to one of them 21 Prove that tan cos-1- tan cos-1 UT2 h' V4 22 Prove that the area of triangle ac sin Β and shew that the area of any triangle is to the area of the triangle formed by joining the points where the lines bisecting the angles meet the opposite sides as 2abc