The argument for #arcsin(x)# (i.e. #x#) must be a value which can be returned by the #sin# function;

since the #sin# function has a range of #[-1,+1]#

#arcsin# has a **domain** of #[-1,+1]#

The **range** of the #arcsin# function is a matter of definition.

In order for #arcsin# to be a function its range is defined to be #[-pi/2,+pi/2]#; without this defined restriction #arcsin# would generate multiple values for a single argument and therefore would not be a function.

For example, noting that #sin(0)=0# and #sin(pi)=0#, it might seem reasonable that #arcsin(0)=0# **and** #arcsin(0)=pi# but this would be contrary to the definition of a function which requires every argument to map into only one value.