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-