Calendar: 1873-1874 Page 551

GENERAL LITERATURE AND SCIENCE 551 52 Show that all the angles which have the same sine as are included in the formula η ν -f1 Assuming that all the angles which have the same cosine as given angle are included in the formula 2ηπ that angle show that all the angles which have the same sine as are included in the formula 2η $κ Show that sin -f- cos sin and that the ambiguity may be replaced by where is the greatest integer contained in being expressed in degrees Μ Show that if θ be less than right angle sin θ θ What are the formulae of verification Write down one and prove it Define logarithm and find the relation between the logarithms of the same number to different bases If are in geometrical progression and 10gt 10g4 logo in arithmetical progression the common difference of the arithmetical progression is Show that sin θ sin θ Lsin θ δ isin β approximately where δ is the circular measure of an angle of 10" and that of small angle less than 10" and that the value of £sin5 -j- given by this formula is correct to places of deci- mais so long as sin θ assuming δ 0005 and μ where μ is the modulus Prove that in any triangle sin sin Β sin