Calendar: 1863-1864 Page 532

532 GENERAL LITERATURE AND SCIENCE III -Crigonomrtrj Having given an angle expressed in degrees it is required to express it in grades and vice versa Prove the rule Divide right angle into two parts such that the number of degrees in one part may be to the number of grades in the other as to 35 Define the cotangent and cosecant of an angle and show that -f cot2 θ cosec2 θ for all values of Θ Prove cos θ cos Θ and find the general value of cos- Sin sin Jfaivi Β sin Β cos Prove this when and Β are acute angles Hence find sin in terms of cos and show priori that we should expect two values in the general expression Find the length of degree of the meridian upon globe 22J inches in diameter Prove the following formulae cot cot Β cot ן--γ י י cot Β cot ii sec tan tan sin sin fill tan2 -x- -1- -S י sin -J- sln Write down with their proper signs the values of the fol- lowing functions sin 30 cos 150 cosec 270 sec 180" tan 720 cot 390 versin 180 The sides of triangle are 30 40 50 feet respectively find the area of the triangle and the radii of the inscribed and circumscribed circles In any triangle prove that- sin sin Β sin T1 ---e ii UaiU iii sin 0""J sin