HYl'KRBOLK FUNCTIONS 



59 



(b) If cosh a = x 



Then ^ (f 



(c) If tanh a = a? 

 Then 



a = log,, {x + Vx z 1 } 



e-e- 



- e~ a = x - e+ x e~ a 



v>\ />~~^fl -L. -rA 

 tcl t/ I J. T~ il/l 



l + fl? 



= 



Then 



1-tf 

 1, 



39. The following table will give a means of comparing the 

 circular functions with the hyperbolic functions : 



