TRIGONOMETRY 



3.25 



i. 



2. 



3- 



4- 

 5- 



sin" 1 x sin" 1 y = sin^ 



- =t 



cos" 1 x cos" 1 y = cos" 1 {^ =F V(i - x*) (i - /)} 

 " 1 



sn" x cos 



" 1 



tan" 1 x tan" 1 y = tan" 1 



tan" 1 # cot" 1 y = tan" 1 



* i 

 = cot" 1 



yV I _ At 



- 4 



i =F xy 



x I 



xy 



HYPERBOLIC FUNCTIONS 



3.30 Formulas for the hyperbolic functions may be obtained from the corre- 

 sponding formulas for the circular functions by replacing x by ix and using the 

 following relations: 



1. sin ix = \i(e x e~ x ) = i sinh x, 



2. cos ix = \(e x + e~ x ) = cosh x. 



3- 

 4- 



5- 

 6. 



7- 



10. 



tan ix 



i tanh x. 



cot 



= i -5 = i coth x. 



i 



sec ix 



= sech x. 



esc ix = 



21 



= i csch x. 



e x - e~ 3 

 sin" 1 ix = i sinh" 1 x = i log (x + A/I + # 2 ). 



cos" 1 i# = i cosh" 1 # = i log (# + \/i + # 2 ) 



tan" 1 ^ = ^* tanh" 1 = i log 



cot" 1 ix = i coth" 1 x = i log 



i + ic 



i - x 



X+ I 

 iC I 



