As #y=sin^(-1)x# means #x=siny#, the graph is similar to graph of #y=sinx# but wave is formed along #y#-axis. The range of #y=sin^(-1)x# is, however, #[-pi/2,pi/2]# and hence its graph is limited between #[-pi/2,pi/2]# along #y#-axis and corresponding values of #x# ranges from #[-1,1]#,
other values are #(-1,-pi/2),(-sqrt3/2,-pi/3),(-1/sqrt2,-pi/4),(-1/2,-pi/6),(0,0),(1/2,pi/6),(1/sqrt2,pi/4),(sqrt3/2,pi/3),(1,pi/2)#.
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^(-1)x# but shifted #2# units to right. The graph appears as follows:
graph{arcsin(x-2) [-10, 10, -5, 5]}
