As y=sin−1x means x=siny, the graph is similar to graph of y=sinx but wave is formed along y-axis. The range of y=sin−1x is, however, [−π2,π2] and hence its graph is limited between [−π2,π2] along y-axis and corresponding values of x ranges from [−1,1],
other values are (−1,−π2),(−√32,−π3),(−1√2,−π4),(−12,−π6),(0,0),(12,π6),(1√2,π4),(√32,π3),(1,π2).
The graph appears as follows:
graph{arcsinx [-10, 10, -5, 5]}
However, in y=sin−1(x−2) x can take values from [1,3] and hence the graph is similar to that of y=sin−1x but shifted 2 units to right. The graph appears as follows:
graph{arcsin(x-2) [-10, 10, -5, 5]}
