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NIST
4 Elementary FunctionsHyperbolic Functions

§4.31 Special Values and Limits

Table 4.31.1: Hyperbolic functions: values at multiples of 12πi.
z 0 12πi πi 32πi
sinhz 0 i 0 -i
coshz 1 0 -1 0
tanhz 0 i 0 -i 1
cschz -i i 0
sechz 1 -1 0
cothz 0 0 1
4.31.1 limz0sinhzz=1,
4.31.2 limz0tanhzz=1,
4.31.3 limz0coshz-1z2=12.