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

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.

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

$\sin \left(\mathrm{ComplexBox}\left(2.3+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[31679.6 +/- 4.36251e-05]}+\text{[-28305.2 +/- 4.09781e-05]}\cdot \mathrm{I}⟩$

$\cos \left(\mathrm{ComplexBox}\left(2.3+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[-28305.2 +/- 4.09781e-05]}+\text{[-31679.6 +/- 4.36251e-05]}\cdot \mathrm{I}⟩$

$\tan \left(\mathrm{ComplexBox}\left(0.3+1.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[0.068039 +/- 3.68229e-11]}+\text{[0.892449 +/- 9.40745e-11]}\cdot \mathrm{I}⟩$

$\arcsin \left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[0.0201834 +/- 4.30376e-09]}+\text{[3.1245 +/- 8.13878e-08]}\cdot \mathrm{I}⟩$

$\arccos \left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[1.55061 +/- 4.47838e-09]}+\text{[-3.1245 +/- 8.13878e-08]}\cdot \mathrm{I}⟩$

$\arctan \left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[1.569 +/- 2.19829e-10]}+\text{[0.088298 +/- 2.50843e-10]}\cdot \mathrm{I}⟩$

$\mathrm{arcsec}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[1.56902 +/- 1.7608e-10]}+\text{[0.0879562 +/- 3.04754e-10]}\cdot \mathrm{I}⟩$

$\mathrm{arccsc}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[0.00177779 +/- 1.45669e-12]}+\text{[-0.0879562 +/- 3.04754e-10]}\cdot \mathrm{I}⟩$

$\mathrm{arccot}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[0.00179862 +/- 2.78037e-10]}+\text{[-0.088298 +/- 2.50843e-10]}\cdot \mathrm{I}⟩$

$\mathrm{sinc}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[3660.19 +/- 4.79469e-06]}+\text{[-779.142 +/- 1.27358e-06]}\cdot \mathrm{I}⟩$

$\mathrm{sinpi}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[1.01169e+15 +/- 8.46511e+06]}+\text{[1.14754e+15 +/- 9.60729e+06]}\cdot \mathrm{I}⟩$

$\mathrm{cospi}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[1.14754e+15 +/- 9.60729e+06]}+\text{[-1.01169e+15 +/- 8.46511e+06]}\cdot \mathrm{I}⟩$

$\mathrm{tanpi}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[2.11957e-31 +/- 1.40926e-39]}+\text{[1 +/- 5.82077e-11]}\cdot \mathrm{I}⟩$

$\mathrm{cotpi}\left(\mathrm{ComplexBox}\left(0.3+1.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[0.000393881 +/- 3.83821e-13]}+\text{[-0.999872 +/- 5.83899e-11]}\cdot \mathrm{I}⟩$

$\mathrm{sincpi}\left(\mathrm{ComplexBox}\left(0.23+11.35\mathrm{I}\right)\right)$

$⟨\text{ComplexBox:}\text{[3.27441e+13 +/- 117611]}+\text{[-2.77093e+13 +/- 104779]}\cdot \mathrm{I}⟩$

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.