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All known subroutines for Arcsine are based on the relation Arcsin N = Arctan [N/(1−N 2)½]. Therefore, Arcsine is not computed as such but as an Arctangent. To avoid the loss of machine time caused by the computation of N/(1−N 2)½, a direct computation of Arcsine is proposed. A subroutine yielding the first six correct significant digits in only five multiplications and divisions is described in detail to illustrate the new method's rapidity. The same number of five operations is necessary to compute, knowing N, the number N/(1−N 2)½.
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