Modern Math CSin

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CSin

Returns the sine of a complex number.

Syntax

CSin( byref z as Complex ) as Complex

Notes

• sin(re)·cosh(im) + i·cos(re)·sinh(im), written out directly.
• It overflows for a large imaginary part, and correctly so: cosh of 750 is beyond float64. The sine of a complex number really is unbounded — it is CTan that stays finite there, and CTan is the one with a guard.
• CSin² + CCos² = 1 holds to within rounding for every operand.
• Spelled with the C prefix because, when this library was a header in namespace FB, a function of the unprefixed name shadowed the intrinsic for every later header — measured, it broke what is now random.tiko — after which the intrinsic could not be called back. The name stayed when the header became std/numeric.

Examples

#import "std/numeric"
using numeric

dim as Complex z = CSet( 3, 4 )

print CToString( CSin( CZero( ) ) )        '' 0+0i   -- exactly zero
print CToString( CSin( z ) )               '' 3.853738037919377-27.016813258003936i
print CIsFinite( CSin( CSet( 1, 750 ) ) )  '' false   -- unbounded, and honestly so

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Library: Math Library
Category: Math Library
Documented under: Members