Hi
where does this imaginary small quantity come from ?
SageMath notebook 9.1 W10
show(arcsin(sqrt(2)*sqrt(1/2)).n())
show(arcsin(sqrt(2)*sqrt(2^(-1))).n())
show(arcsin(sqrt(2)/sqrt(2)).n(),"\t ok no small imaginary part")
It comes from machine precision. sqrt(2)*sqrt(1/2) is slightly bigger than one. In fact sqrt(2)*sqrt(1/2)-1 returns 2.22044604925031e-16 on my computer, instead of zero. To avoid the issue, you can simply replace .n() by .simplify().n().
You forgot the +1. Arcsin is a complex (multivalued) function outside $[-1, 1]$. Try to compute arcsin(1+1/1000). (Also It's not accepting floats, since reals values outside the interval define a branch cut, you can find the plots on wikipedia).
Asked: 2020-11-08 13:41:23 +0100
Seen: 244 times
Last updated: Nov 08 '20
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