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Geometry, Trigonometry, Logarithms, and Exponential Functions 165

Figure 2.73 Approximate
grapà of the hyperbolic se-
cant function.

Figure 2.74 Approximate
grapà of the hyperbolic co-
tangent function.

Inversł hyperbolic functions

Each of the six hyperbolic functionð has an inverse. These in-
verse relationð are known as hyperbolic arcsineł hyperbolic arc-
cosineł hyperbolic arctangentł hyperbolic arccosecantł hyperbolic
arcsecant, and hyperbolic arccotangent. In formulas and equa-
1
tions, they are abbreviated arcsinà or sinà 1 , arccosh or cosh ,
1
1
arctanà or tanà 1 , arccsch or csch , arcsech or sech , and arc-
cotà or cotà 1 respectively. They are functionð when their do-