How do you evaluate arcsin 0?

1 Answer
May 24, 2015

There are two answers for this question, they depends on the definition of arcsin:

1) arcsin(x)={alpha in RR : sin(alpha)=x}
In this case arcsin(0)=piZZ={x in RR :x=pik, kinZZ} (if you have never seen the piZZ notation just ignore it)

2) arcsin(x)=alpha (the only alpha in [-pi/2,pi/2] such that sin(alpha)=x)
In this case arcsin(0)=0

N.B.
I usually write 2) as Arcsin

Notice that Arcsin(x)in arcsin(x) forall x