Unformatted text preview: GRAPHS OF HYPERBOLIC FUNCTIONS y = slnhx y=ooshx .1 INVERSE a HYPERBOLIC FUNCTIONS Ifx = slnh y, theny = slnrr1 a Is called the
Inverse hyperbolic slne of
x. Slmllarly we deflne
the other Inverse
hyperbollc functlons. The
Inverse hyperbollc
functlons are multlple
valued and as In the
case of Inverse
trlgonometrlc functlons
we restrlct ourselves to
prlnclpal values for whlch
they can be oonsldered
as slnglevalued. The followlng list shows the prlnclpal values [unless otherwlse lndlcated] of the Inverse hyperbollc functlons expressed In terms of logarlthmlc functlons whlch are taken as real valued.
slnh'1 x = In (x +I/5‘ﬁ) oosh’1 x = In (x + m)
tam1x = Vzln((1 + x)/(1  x))
(:oth'1 x = V:ln((x + 1)/(x  1)) sech'1 x = In ( 1]): + :1;_,‘) 0 < x s 1 [sech'1 a; > o Is prlnclpal value] [email protected]<X<@ x z 1 [oosh’1 x > 0 Is prlnclpal value] 1<x<1 X>10fX<1 (sch‘1 x = In(1/x + "5’, I) x s o GRAPHS OF INVERSE HYPERBOLIC FUNCTIONS y = slnh‘lx y = cosh'lx
v ...
View
Full Document
 Fall '08
 WILKENING

Click to edit the document details