Circular - Maple Help

ComplexBox

 Circular
 circular functions for ComplexBox objects
 sin
 compute the sine of a ComplexBox object
 cos
 compute the cosine of a ComplexBox object
 tan
 compute the tangent of a ComplexBox object
 sec
 compute the secant of a ComplexBox object
 csc
 compute the cosecant of a ComplexBox object
 cot
 compute the cotangent of a ComplexBox object
 sinc
 compute the sinc of a ComplexBox object
 sinpi
 compute the sine of Pi times a ComplexBox object
 cospi
 compute the cosine of Pi times a ComplexBox object
 tanpi
 compute the tangent of Pi times a ComplexBox object
 cotpi
 compute the cotangent of Pi times a ComplexBox object
 sincpi
 compute the sinc of Pi times a ComplexBox object
 arcsin
 compute the inverse sine of a ComplexBox object
 arccos
 compute the inverse cosine of a ComplexBox object
 arctan
 compute the inverse tangent of a ComplexBox object
 arccot
 compute the inverse cotangent of a ComplexBox object
 arcsec
 compute the inverse secant of a ComplexBox object
 arccsc
 compute the inverse cosecant of a ComplexBox object

 Calling Sequence sin( b ) cos( b ) tan( b ) sec( b ) csc( b ) cot( b ) sinc( b ) sinpi( b ) cospi( b ) tanpi( b ) cotpi( b ) sincpi( b ) arcsin( b ) arccos( b ) arctan( b ) arcsec( b ) arccsc( b ) arccot( b )

Parameters

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

Description

 • These are the standard circular (i.e., trigonometric) functions defined for ComplexBox objects.

 sin cos tan sec csc cot arcsin arccos arctan arcsec arccsc arccot

 • They override the standard Maple procedures for ComplexBox objects.
 • Additionally, via "arblib", there are a number of variations that are not defined for standard numerics in Maple.

 sinc( b ) sin( b ) / b sinpi( b ) sin( Pi*b ) cospi( b ) cos( Pi*b ) tanpi( b ) tan( Pi*b ) cotpi( b ) cot( Pi*b ) sincpi( b ) sinc( Pi*b )

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

Examples

 > $\mathrm{sin}\left(\mathrm{ComplexBox}\left(2.3+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[31679.6 +/- 4.36251e-05]}}{+}{\text{[-28305.2 +/- 4.09781e-05]}}{\cdot }{I}{⟩}$ (1)
 > $\mathrm{cos}\left(\mathrm{ComplexBox}\left(2.3+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[-28305.2 +/- 4.09781e-05]}}{+}{\text{[-31679.6 +/- 4.36251e-05]}}{\cdot }{I}{⟩}$ (2)
 > $\mathrm{tan}\left(\mathrm{ComplexBox}\left(0.3+1.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.068039 +/- 3.68229e-11]}}{+}{\text{[0.892449 +/- 9.40745e-11]}}{\cdot }{I}{⟩}$ (3)
 > $\mathrm{arcsin}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.0201834 +/- 4.30376e-09]}}{+}{\text{[3.1245 +/- 8.13878e-08]}}{\cdot }{I}{⟩}$ (4)
 > $\mathrm{arccos}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1.55061 +/- 4.47838e-09]}}{+}{\text{[-3.1245 +/- 8.13878e-08]}}{\cdot }{I}{⟩}$ (5)
 > $\mathrm{arctan}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1.569 +/- 2.19829e-10]}}{+}{\text{[0.088298 +/- 2.50843e-10]}}{\cdot }{I}{⟩}$ (6)
 > $\mathrm{arcsec}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1.56902 +/- 1.7608e-10]}}{+}{\text{[0.0879562 +/- 3.04754e-10]}}{\cdot }{I}{⟩}$ (7)
 > $\mathrm{arccsc}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.00177779 +/- 1.45669e-12]}}{+}{\text{[-0.0879562 +/- 3.04754e-10]}}{\cdot }{I}{⟩}$ (8)
 > $\mathrm{arccot}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.00179862 +/- 2.78037e-10]}}{+}{\text{[-0.088298 +/- 2.50843e-10]}}{\cdot }{I}{⟩}$ (9)
 > $\mathrm{sinc}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[3660.19 +/- 4.79469e-06]}}{+}{\text{[-779.142 +/- 1.27358e-06]}}{\cdot }{I}{⟩}$ (10)
 > $\mathrm{sinpi}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1.01169e+15 +/- 8.46511e+06]}}{+}{\text{[1.14754e+15 +/- 9.60729e+06]}}{\cdot }{I}{⟩}$ (11)
 > $\mathrm{cospi}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[1.14754e+15 +/- 9.60729e+06]}}{+}{\text{[-1.01169e+15 +/- 8.46511e+06]}}{\cdot }{I}{⟩}$ (12)
 > $\mathrm{tanpi}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[2.11957e-31 +/- 1.40926e-39]}}{+}{\text{[1 +/- 5.82077e-11]}}{\cdot }{I}{⟩}$ (13)
 > $\mathrm{cotpi}\left(\mathrm{ComplexBox}\left(0.3+1.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[0.000393881 +/- 3.83821e-13]}}{+}{\text{[-0.999872 +/- 5.83899e-11]}}{\cdot }{I}{⟩}$ (14)
 > $\mathrm{sincpi}\left(\mathrm{ComplexBox}\left(0.23+11.35I\right)\right)$
 ${⟨}{\text{ComplexBox:}}{\text{[3.27441e+13 +/- 117611]}}{+}{\text{[-2.77093e+13 +/- 104779]}}{\cdot }{I}{⟩}$ (15)

Compatibility

 • The ComplexBox[Circular], ComplexBox:-sin, ComplexBox:-cos, ComplexBox:-tan, ComplexBox:-sec, ComplexBox:-csc, ComplexBox:-cot, ComplexBox:-sinc, ComplexBox:-sinpi, ComplexBox:-cospi, ComplexBox:-tanpi, ComplexBox:-cotpi, ComplexBox:-sincpi, ComplexBox:-arcsin, ComplexBox:-arccos, ComplexBox:-arctan, ComplexBox:-arccot, ComplexBox:-arcsec and ComplexBox:-arccsc commands were introduced in Maple 2022.