424 A NZW and VNIFERSAL SOLUTION - 



Suppofe cof ^^ = J V°of a ' ^^^^' ^^^'^ I — cof 4- = 2 fin ' - 



fin '— ^ 



; = tan ^ — , therefore 



col - 



2 



fin ^ = tan ^ V -L = tan - X fin 45 ° : We fhall alfo have 



2 2 v/2 2 ^-^ 



^ 4^ I — cof A 

 we have 2 fin — = i^_cofA 



2 fin 



^ _ i-cofA _ (i-cofA) - ^ Ci - cof A)- ^j^^^^^^ 

 2 — I + cof A ~ I — cof * A fin ^ A 



4, _ I — cof A _^ Subftitute now, for cof -4/, its value 

 "" 2 "" fin A ^v/2 



2 cof A 



I — cof A 



col 



^ ; and for fin f , its value -jj^,^— X — 5 and we 

 Ihall eafily obtain, 



rip "' ^ 



f ^2 X fin <P X cof A = col !— - — X fin A, 



whence ^^ = tan A = ^ x 



fin (p 



cof 



^ — m 



X 1/2. 



Hence we have another general rule for computing | when p 

 is given, which is this : Take tan A = ^ x l^i-^ — X fee 45° ) 



cof 



(p — m 



J, A o 



then fin J = tan - X 45 . 



Taking m = go", and <p = 90°, this rule coincides with 

 that already given in Art. io. : And it may be of ufe, not only 

 when ?« is exadly a right angle, but alfo when it is very nearly 



fo. 



The detail with which we have difcuffed the rules and for- 

 mulas of computation that have been deduced from the analyfis, 

 leaves no difficulty in applying them to pradice, Thefe rules 



are 



