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The inverse functions of the six hyperbolic functions: sinh, cosh, tanh, coth, sech, and cosech. The inverse hyperbolic functions are defined in a analogous way in which the inverse trigonometric functions are defined.
Read Denoted inverse hyperbolic sine of x arsinh x, or arsh x or sinh-1x inverse hyperbolic cosine of x arcosh x, or arch x or cosh-1x inverse hyperbolic tangent of x artanh x, or arth x or tanh-1x inverse hyperbolic cotangent of x arcoth x, or arcth x or coth-1x inverse hyperbolic secant of x arsec x or sech-1x inverse hyperbolic cosecant of x arcsch x, or arcosech x or cosech-1x The frequently used inverse hyperbolic functions are given by the following formulas:
sinh-1x = ln[x + (x2 + 1)1/2] for all x
cosh-1x = ln[x + (x2 - 1)1/2] for x > 1
tanh-1x = ln{[(1 + x)/(1 - x)]1/2} for -1 < x < 1
