 Hyperbolic - Maple Help

RealBox

 Hyperbolic
 hyperbolic functions for RealBox objects
 sinh
 compute the hyperbolic sine of a RealBox
 cosh
 compute the hyperbolic cosine of a RealBox
 tanh
 compute the hyperbolic tangent of a RealBox
 sech
 compute the hyperbolic secant of a RealBox
 csch
 compute the hyperbolic cosecant of a RealBox
 coth
 compute the hyperbolic cotangent of a RealBox
 arcsinh
 compute the inverse hyperbolic sine of a RealBox
 arccosh
 compute the inverse hyperbolic cosine of a RealBox
 arctanh
 compute the inverse hyperbolic tangent of a RealBox
 arcsech
 compute the inverse hyperbolic secant of a RealBox
 arccsch
 compute the inverse hyperbolic cosecant of a RealBox
 arccoth
 compute the inverse hyperbolic cotangent of a RealBox
 sinhcosh
 compute simultaneously the hyperbolic sine and cosine of a RealBox Calling Sequence sinh( b ) cosh( b ) tanh( b ) sech( b ) csch( b ) coth( b ) arcsinh( b ) arccosh( b ) arctanh( b ) arcsech( b ) arccsch( b ) arccoth( b ) sinhcosh( b ) Parameters

 b - RealBox object precopt - (optional) equation of the form precision = n, where n is a positive integer Description

 • The hyperbolic functions and their important inverses are defined as methods for RealBox objects.
 • Apart from sinhcosh, which returns an expression sequence of two RealBox objects, each of these computes a RealBox representing the value of the named function on the values in the RealBox input.

 sinh cosh tanh sech csch coth arcsinh arccosh arctanh arcsech arccsch arccoth sinhcosh

 • Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision. Examples

 > $a≔\mathrm{RealBox}\left(0.34\right)$
 ${a}{≔}{⟨}{\text{RealBox:}}{0.34}{±}{2.91038ⅇ-11}{⟩}$ (1)
 > $b≔\mathrm{RealBox}\left(2.3\right)$
 ${b}{≔}{⟨}{\text{RealBox:}}{2.3}{±}{2.32831ⅇ-10}{⟩}$ (2)
 > $\mathrm{sinh}\left(b\right)$
 ${⟨}{\text{RealBox:}}{4.93696}{±}{1.66822ⅇ-09}{⟩}$ (3)
 > $\mathrm{cosh}\left(b\right)$
 ${⟨}{\text{RealBox:}}{5.03722}{±}{1.66822ⅇ-09}{⟩}$ (4)
 > $\mathrm{tanh}\left(b\right)$
 ${⟨}{\text{RealBox:}}{0.980096}{±}{6.79399ⅇ-11}{⟩}$ (5)
 > $\mathrm{sech}\left(b\right)$
 ${⟨}{\text{RealBox:}}{0.198522}{±}{6.40579ⅇ-11}{⟩}$ (6)
 > $\mathrm{csch}\left(b\right)$
 ${⟨}{\text{RealBox:}}{0.202554}{±}{6.43682ⅇ-11}{⟩}$ (7)
 > $\mathrm{coth}\left(b\right)$
 ${⟨}{\text{RealBox:}}{1.02031}{±}{1.26273ⅇ-10}{⟩}$ (8)
 > $\mathrm{arcsinh}\left(b\right)$
 ${⟨}{\text{RealBox:}}{1.57028}{±}{2.16758ⅇ-10}{⟩}$ (9)
 > $\mathrm{arccosh}\left(b\right)$
 ${⟨}{\text{RealBox:}}{1.47504}{±}{2.33821ⅇ-10}{⟩}$ (10)
 > $\mathrm{arctanh}\left(a\right)$
 ${⟨}{\text{RealBox:}}{0.354093}{±}{6.73914ⅇ-11}{⟩}$ (11)
 > $\mathrm{arcsech}\left(a\right)$
 ${⟨}{\text{RealBox:}}{1.74172}{±}{3.01167ⅇ-10}{⟩}$ (12)
 > $\mathrm{arccsch}\left(a\right)$
 ${⟨}{\text{RealBox:}}{1.79968}{±}{2.78979ⅇ-10}{⟩}$ (13)
 > $\mathrm{arccsch}\left(b\right)$
 ${⟨}{\text{RealBox:}}{0.422133}{±}{9.88916ⅇ-11}{⟩}$ (14)

Unlike the other functions defined above, the sinhcosh( b ) command returns an expression sequence of two RealBox objects representing, respectively, the values sinh( b ) and cosh( b ) of the RealBox argument b.

 > $\mathrm{sinhcosh}\left(b\right)$
 ${⟨}{\text{RealBox:}}{4.93696}{±}{1.66822ⅇ-09}{⟩}{,}{⟨}{\text{RealBox:}}{5.03722}{±}{1.66822ⅇ-09}{⟩}$ (15) Compatibility

 • The RealBox:-sinh, RealBox:-cosh, RealBox:-tanh, RealBox:-sech, RealBox:-csch, RealBox:-coth, RealBox:-arcsinh, RealBox:-arccosh and RealBox:-arctanh commands were introduced in Maple 2022.