TRIGONOMETRY 



3.172 n an odd integer: 



(n 2 - i 2 ) . (n 2 - i 2 ) (n 2 - 3 2 ) , 

 sin nx = n \ sm x : sm 3 x H p sin 5 x . 



6 7 



cos nx = cos 



[ I (n 2 - i 2 ) 

 1 2! 



sm 



rc 2 - i 2 ) (rc 2 - 3 2 ) , 

 - J - U sm 4 *-. 



3.173 n an even integer: 



n r / \ 



sin nx = (-i) 2 cos x < 2"" 1 sin"" 1 of j 2"~ 3 sin"" 3 x 



, ( w 3) ( n 4) _* _c '( 4) (n 5) ( 



2! 



3!. 



cos nx = (-1)2 ^ 2"" 1 sin" x - - ( 2"" 3 sin 71 " 2 x + t ~' 2"" sin -* ^ 



n ~ 5 n ~ 4 



3.174 n an odd integer: 



n(n - 3) ( - 5) . n _7 01 - 



sm 



n-6 



sin wx = (-1) 2 { 2"" 1 sin" x - 2"" 3 sin"" 2 x 



2! 



w(w - 3) (n - 5) n _ 7 . 

 ~3l~ 



M I f n _ 2 



/-*/-vc /i^/v* ^ T^ i r*/^C 'V / O^ 1 CITl ^ 1 'V - - r\Tl 3 C1TI ^ ' -V 



COS WX = \^ L) 2 LUb A/ \ sill a/ . ^ Mil *v 



( - 3) (n - 4) 5 . 5 ( - 4) ( - 5) ( - 



"IT 3! 



3.175 n any integer: 



,n-7 



+ . . 



sn nx = sn x 2 



n ~ l 



n ~ 3 n ~ 



i 



2"~ COS 



(n - 3) (n - 4) 2 ,_ f 



- 4) ^ - 5 ) (^ " 6) n _ 7 



cos nx = 2"" 1 cos" x - 2"" 3 cos"" 2 x + n 3 2"" 5 cos"" 4 x 



3! 



