About the Project
4 Elementary FunctionsHyperbolic Functions

§4.30 Elementary Properties

Table 4.30.1: Hyperbolic functions: interrelations. All square roots have their principal values when the functions are real, nonnegative, and finite.
sinhθ=a coshθ=a tanhθ=a cschθ=a sechθ=a cothθ=a
sinhθ a (a21)1/2 a(1a2)1/2 a1 a1(1a2)1/2 (a21)1/2
coshθ (1+a2)1/2 a (1a2)1/2 a1(1+a2)1/2 a1 a(a21)1/2
tanhθ a(1+a2)1/2 a1(a21)1/2 a (1+a2)1/2 (1a2)1/2 a1
cschθ a1 (a21)1/2 a1(1a2)1/2 a a(1a2)1/2 (a21)1/2
sechθ (1+a2)1/2 a1 (1a2)1/2 a(1+a2)1/2 a a1(a21)1/2
cothθ a1(a2+1)1/2 a(a21)1/2 a1 (1+a2)1/2 (1a2)1/2 a