Inverse Hyperbolic Functions

In this post we discuss about inverse Hyperbolic Function and also their domain and Range. The Inverse Hyperbolic Functions are expressed in terms of natural ;logarithms.

Function	Formulas
Sinh^-1x	$ln(x+\sqrt{x^2+1}), \forall \,\,\ x$
Cosh^-1x	$ln(x+\sqrt{x^2-1}), \forall \,\,\ x\geq 1$
Tanh^-1x	$\frac{1}{2}ln(\frac{1+x}{1-x}) , \|x\| < 1$
Cosech^-1x	$ln(\frac{1}{x}+\frac{\sqrt{1+x^2}}{\|x\|}) , x \neq 0$
Sech^-1x	$ln(\frac{1}{x}+\frac{\sqrt{1-x^2}}{\|x\|}) , 0 < x \leq 1$
Coth^-1x	$\frac{1}{2}ln(\frac{x+1}{x-1}) , \|x\| < 1$

PAKMATH Knowledge Learning Point

Inverse Hyperbolic Functions

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