Circular - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim

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.
 • For more information on Maple 2022 changes, see Updates in Maple 2022.

 See Also