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arcsin() return value with imaginary part ?

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")

arcsin() return value with imaginary part ?

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")