the domain of f(x)=sinx is (-infinity,+infinity), the range is [-1,1]
the domain of sin-1x is [-1,+1], and for sin-1x to be a function the range is limited to (-π/2,+-π/2]
if the value of x in sin-1x is 1/2, then y=sin-1x has multiple values, [π/6+2kπ], and [2m+1)π-π/6]
where k and m are 0,+/-1,+/-2,...
k=0 and m=0 give "principal value" returned in calculator)=π/6 for x=1/2 and viable 5π/6 for third quadrant result.