62 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



sin 2x i cos 2x 



3.03 tan x = - tan (- x) 



i + cos 2x sin 2x 



i - cos 2x _ sin (x + y) + sin (x y) 

 i + cos 2x cos (x + y) + cos (x y) 1 



cos (x y) cos (x + y) 



sin (* + ?)- sin (x - y) 



COt X 2 COt 2#, 



'T* 



tan - tan - 2 tan - 



_ 2 _ 2 ___ 2_ 



"""* ~~# ~ ""#' 



i - tan - i + tan - i - tan 2 - 



222 



i tan - i + tan - 

 2 2 



3.04 The values of five trigonometric functions in terms of the sixth are given 

 in the following table. (For signs, see 3.05.) 



3.05 The trigonometric functions are periodic, the periods of the sin, cos, sec, 

 csc being 2?r, and those of the tan and cot, TT. Their signs may be determined 

 from the following table. In using formulas giving any of the trigonometric 



