Calendar: 1871-1872 Page 580

580 the school 12 Prove that the eonvergeuts to continued fraction taken in order are alternately less and greater than the continued fraction and that each is nearer the true value than the one pre- ceding Convert Vr into continued fraction The number 301 is perfect square in what scale is it expressed 13 If η be prime number and JV prime to show that Λ11-1 is divisible by Prove also that Nx יי will be divisible by UP 14 Find the whole number of permutations which can be made of the letters of the word "treatise taking any number together Cvtgonoinrtri Define the circular measure of an angle An angle is measured by the geometric mean between the number of units of circular measure and French grades which it contains prove that the number of degrees in the unit of the system is ν 7r ז ρ sin 7r cos θ י race the changes in sign ot----- as θ varies from cos π sin to 7r Express sin and cos in terms of sin Show priori that each will have values Determine the limits between which lies when cos -f- sin is negative Show that ηπ is the general solution of each of the equations sin2 θ sin2 cos2 θ cos2 tan2 θ tan2a Find general formula for all angles whose sines are equal and of the same sign and cosines equal but of opposite sign Solve the equations sin 6Θ sin 26