Calendar: 1870-1871 Page 516

516 general literature and science Division Second Year -Division First Year IV -Crtgonomrtri coe Trace the changes of -7- from to 180 ס cos Prove the formula sin -f- sin cos Β cos sin Β when and Β are each between 90 and 180 Deduce the formula for cos Investigate general formula for all angles the sines of which are equal to the sine of Find the general value of an angle such that its cosine is to its tangent as to Prove that tan-'i tan 'i tan β tan 'I ta -י ta" 11 Prove also the formulae cos 45 cos 45 sin cos cos β cos -f- δ cos cos cos2 β where α β γ δ are the angles of quadrilateral inscribed in circle If be the angles of triangle prove that Β Β COS Α ך COS cos sln cos τ sin cos Ο -Β sin דד COS If the sides of triangle in Arithmetical Progression so also are the cotangents of the semi-angles In any triangle the sum of the cosines of the halves of any two of the angles is greater than the cosine of half the third Show that the circular measure of an angle between zero and right angle is greater than its sine and less than its tangent