TRIGONOMETRY 69 



3.182 n an odd integer: 



n i 



sin n x = _* | sin nx - n sin (n - 2)x + f sin (n - 4)x 

 n(n - i) (n ~j). sin / _ 6 ^ , , (_ I ) Z - 1 w! 



o * 



if / x n(n i) 

 cos n x = { cos nx + n cos (w - 2)x H j - cos (n - 4)x 



w(w i) (n 2) , , 

 + ^ ^ cos (n - 6)* + 



3.183 



sin? x = %(i cos 2x). 



sin 3 x = i(3 sin x sin 3^). 



sin 4 x = | (cos 4X - 4 cos 2x + 3). 



sin 5 x = -reCsin 5^-5 sin 3^ + 10 sin ^). 



sin 6 x = -j^(cos 6x 6 cos $x+ 15 cos 2X 10). 



3184 



cos 2 x = i( T + cos 2X )- 



cos 3 ^ = 1(3 cos ^ + cos 3#). 



cos 4 x = |(3 + 4 cos 2X + cos 4^). 



cos 5 x = iV( 10 cos ^ + 5 cos 3^ + cos 5 X )' 



cos 6 jc = ^2 (10 + 15 cos 2x + 6 cos 4# + cos 6x). 



nl 



cos x 



INVERSE CIRCULAR FUNCTIONS 



3.20 The inverse circular and logarithmic functions are multiple valued; i.e., if 



7T 



o<sin~ 1 x<, 



2 



the solution of x = sin 6 is : 



, 6 = 2mr + sin" 1 x, 



where n is a positive integer. In the following formulas the cyclic constants are 

 omitted. 



