Circular - Maple Help

RealBox

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

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

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

 function definition 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

 > $\mathrm{sin}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{0.745705}{±}{2.16318ⅇ-10}{⟩}$ (1)
 > $\mathrm{cos}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{-0.666276}{±}{2.35566ⅇ-10}{⟩}$ (2)
 > $\mathrm{tan}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{-1.11921}{±}{6.61871ⅇ-10}{⟩}$ (3)
 > $\mathrm{arcsin}\left(\mathrm{RealBox}\left(0.23\right)\right)$
 ${⟨}{\text{RealBox:}}{0.232078}{±}{7.55526ⅇ-11}{⟩}$ (4)
 > $\mathrm{arccos}\left(\mathrm{RealBox}\left(0.23\right)\right)$
 ${⟨}{\text{RealBox:}}{1.33872}{±}{2.50176ⅇ-10}{⟩}$ (5)
 > $\mathrm{arctan}\left(\mathrm{RealBox}\left(0.23\right)\right)$
 ${⟨}{\text{RealBox:}}{0.226068}{±}{2.92822ⅇ-11}{⟩}$ (6)
 > $\mathrm{arcsec}\left(\mathrm{RealBox}\left(1.23\right)\right)$
 ${⟨}{\text{RealBox:}}{0.621496}{±}{4.40417ⅇ-10}{⟩}$ (7)
 > $\mathrm{arccsc}\left(\mathrm{RealBox}\left(1.23\right)\right)$
 ${⟨}{\text{RealBox:}}{0.9493}{±}{3.8221ⅇ-10}{⟩}$ (8)
 > $\mathrm{arccot}\left(\mathrm{RealBox}\left(1.23\right)\right)$
 ${⟨}{\text{RealBox:}}{0.682623}{±}{1.62742ⅇ-10}{⟩}$ (9)
 > $\mathrm{sinc}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{0.32422}{±}{1.51896ⅇ-10}{⟩}$ (10)
 > $\mathrm{sinpi}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{0.809017}{±}{5.3933ⅇ-10}{⟩}$ (11)
 > $\mathrm{cospi}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{0.587785}{±}{7.23958ⅇ-10}{⟩}$ (12)
 > $\mathrm{tanpi}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{1.37638}{±}{2.2842ⅇ-09}{⟩}$ (13)
 > $\mathrm{cotpi}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{0.726543}{±}{1.2025ⅇ-09}{⟩}$ (14)
 > $\mathrm{sincpi}\left(\mathrm{RealBox}\left(2.3\right)\right)$
 ${⟨}{\text{RealBox:}}{0.111964}{±}{8.01149ⅇ-11}{⟩}$ (15)

Compatibility

 • The RealBox:-sin, RealBox:-cos, RealBox:-tan, RealBox:-sec, RealBox:-csc, RealBox:-cot, RealBox:-sinc, RealBox:-sinpi, RealBox:-cospi, RealBox:-tanpi, RealBox:-cotpi, RealBox:-sincpi, RealBox:-arcsin, RealBox:-arccos and RealBox:-arctan commands were introduced in Maple 2022.