Only that part of the sine curve coincident with its principal branch "survives" this graphing of the inverse of the inverse. Hence, it can be inferred from the graph that the domain of the principal branch is the interval $\left[-\mathrm{\π}\/2\,\mathrm{\π}\/2\right]$.

Alternatively, use the Context Panel to launch the Plot Builder as per the following, selecting the option 2-D plot (parametric).

$\left[\arcsin \left(x\right)\,x\right]$$\to$

Obtain Figure A-7.7(c) by executing the command

$\mathrm{plot}\left(\left[\arcsin \left(x\right)\,x\,x\=-3..3\right]\,\mathrm{labels}\=\left[x\,\mathrm{typeset}\left(\sin \left(x\right)\right)\right]\,\mathrm{tickmarks}\=\left[\mathrm{piticks}\,\left[-1\,0\,1\right]\right]\,\mathrm{view}\=\left[-\mathrm{\pi }\/2..\mathrm{\pi }\/2\,-1..1\right]\right)$