Mathematical Methods for Physics and Engineering : A Comprehensive Guide

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3.7 HYPERBOLIC FUNCTIONS


sechx

coshx

x

1


2


3


4


− 2 − 1 1 2


Figure 3.11 Graphs of coshxand sechx.

cosechx

cosechx

sinhx

x

2


4


− 2


− 4


− 2 − 1 1 2


Figure 3.12 Graphs of sinhxand cosechx.

Hence, by the definitions given in the previous subsection,


coshx=cosix, (3.44)

isinhx=sinix, (3.45)

cosx=coshix, (3.46)

isinx= sinhix. (3.47)

These useful equations make the relationship between hyperbolic and trigono-

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