Hyperbolic - Maple Help

ComplexBox

 Hyperbolic
 hyperbolic functions for ComplexBox objects
 sinh
 compute the hyperbolic sine of a ComplexBox object
 cosh
 compute the hyperbolic cosine of a ComplexBox object
 tanh
 compute the hyperbolic tangent of a ComplexBox object
 sech
 compute the hyperbolic secant of a ComplexBox object
 csch
 compute the hyperbolic cosecant of a ComplexBox object
 coth
 compute the hyperbolic cotangent of a ComplexBox object
 arcsinh
 compute the inverse hyperbolic sine of a ComplexBox object
 arccosh
 compute the inverse hyperbolic cosine of a ComplexBox object
 arctanh
 compute the inverse hyperbolic tangent of a ComplexBox object
 sinhcosh
 compute simultaneously the hyperbolic sine and hyperbolic cosine of a ComplexBox object

 Calling Sequence sinh( b ) cosh( b ) tanh( b ) sech( b ) csch( b ) coth( b ) arcsinh( b ) arccosh( b ) arctanh( b ) sinhcosh( b )

Parameters

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

Description

 • These are the hyperbolic functions defined for ComplexBox objects. Apart from sinhcosh, which returns an expression sequence of two ComplexBox objects, each of these computes a ComplexBox representing the value of the named function on the values in the ComplexBox input.

 sinh cosh tanh sech csch coth arcsinh arccosh arctanh sinhcosh

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

Examples

 > $a≔\mathrm{ComplexBox}\left(0.34+1.1I\right)$
 ${a}{≔}{⟨}{\text{ComplexBox:}}{\text{[0.34 +/- 2.91038e-11]}}{+}{\text{[1.1 +/- 1.16415e-10]}}{\cdot }{I}{⟩}$ (1)
 > $b≔\mathrm{ComplexBox}\left(2.3-4.4I\right)$
 ${b}{≔}{⟨}{\text{ComplexBox:}}{\text{[2.3 +/- 2.32831e-10]}}{+}{\text{[-4.4 +/- 4.65661e-10]}}{\cdot }{I}{⟩}$ (2)
 > $\mathrm{sinh}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-1.51729 +/- 2.9924e-09]}}{+}{\text{[4.79343 +/- 3.07814e-09]}}{\cdot }{I}{⟩}$ (3)
 > $\mathrm{cosh}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-1.5481 +/- 3.04039e-09]}}{+}{\text{[4.69802 +/- 3.05774e-09]}}{\cdot }{I}{⟩}$ (4)
 > $\mathrm{tanh}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1.01637 +/- 1.36325e-10]}}{+}{\text{[-0.0119527 +/- 2.29125e-11]}}{\cdot }{I}{⟩}$ (5)
 > $\mathrm{sech}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-0.0632704 +/- 1.31738e-10]}}{+}{\text{[-0.192006 +/- 1.39835e-10]}}{\cdot }{I}{⟩}$ (6)
 > $\mathrm{csch}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-0.0600215 +/- 1.19315e-10]}}{+}{\text{[-0.18962 +/- 1.16933e-10]}}{\cdot }{I}{⟩}$ (7)
 > $\mathrm{coth}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.983758 +/- 7.77339e-11]}}{+}{\text{[0.0115692 +/- 2.25103e-11]}}{\cdot }{I}{⟩}$ (8)
 > $\mathrm{arcsinh}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.2898 +/- 2.36325e-08]}}{+}{\text{[-1.08066 +/- 2.28804e-08]}}{\cdot }{I}{⟩}$ (9)
 > $\mathrm{arccosh}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.30138 +/- 5.87225e-10]}}{+}{\text{[-1.09732 +/- 4.70888e-10]}}{\cdot }{I}{⟩}$ (10)
 > $\mathrm{arctanh}\left(a\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.150593 +/- 2.42726e-10]}}{+}{\text{[0.858865 +/- 3.60329e-10]}}{\cdot }{I}{⟩}$ (11)

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

 > $\mathrm{sinhcosh}\left(b\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-1.51729 +/- 2.9924e-09]}}{+}{\text{[4.79343 +/- 3.07814e-09]}}{\cdot }{I}{⟩}{,}{⟨}{\text{ComplexBox:}}{\text{[-1.5481 +/- 3.04039e-09]}}{+}{\text{[4.69802 +/- 3.05774e-09]}}{\cdot }{I}{⟩}$ (12)

Compatibility

 • The ComplexBox[Hyperbolic], ComplexBox:-sinh, ComplexBox:-cosh, ComplexBox:-tanh, ComplexBox:-sech, ComplexBox:-csch, ComplexBox:-coth, ComplexBox:-arcsinh, ComplexBox:-arccosh, ComplexBox:-arctanh and ComplexBox:-sinhcosh commands were introduced in Maple 2022.