T R I 



1 3 5 7 ... n 1 2 * 



JVote. If n be sren the last term must alway be ' '-- '-- - 



1.2.3... 

 2 



Ext. 2 (cos. A)g = cos. 2 A 4. 1. 



2 (cos. A)s cos. 3 A 4- 3 cos. A. 



23 (cos. A)4 = cos. 4 A 4- 4 cos. 2 A -J- 3. 



24 (cos. A)* = cos. 5 A 4- 5 cos. 3 A 4. 10 cos. A. 



25 (cos. A) 6 = cos. 6 A -f 6 cos. 4 A 4. 15 cos. 2 A 4. 10. 



&c. &c. 



2. 2 n ~ l (sin. A) n 4- cos. n A qp cos. ( 2) . A -f n. n ~ l cos. 



(n 4) A &c. where the upper sign must be used when n is 4, 8, 12, &c. 

 and the lower when n is 2, 6, 10, &c., and in both cases the last term is 

 as before. 



3. 2 71 " (sin. A) n = 4. sin. n A ip sin. ( 2) A + n. 



(n 4) A, &c., where the upper sign must be used when n is 1, 5, 9, &c., 

 and the lower when n is 3, 7, 11, &c. 

 Exa. 2 (sin. A) cos. 2 A + 1. 



2g (sin. A) 3 = sin. 3 A 4- 3 sin. A. 

 2s (sin. A)4 = cos. 4 A 4 cos. 2 A 4. 3. 



24 (sin. A)5 - sin. 5 A 5 sin. 3 A 4- 10 sin. A, 



25 (sin. A)6 - cos. C A 4. 6 cos. 4 A 15 cos. 2 A 4. 10. 

 Series for the sine and cosine in terms of the arc, 



2. 



Value of the sine in some of the most simple catet. 

 Sin. - 0. 



Sin - 9 = 



sin. iso = 



Sin. 180-1. (V"5 l 

 S;n. 27o - 1 

 Sin. 300 - 1 . 

 SSO 



