How do you graph #y=sin^-1(x/2)# over the interval #-2<=x<=2#?
As per the convention, the range for y is the range for #sin^(-1)(x/2=
[sin^(-1), sin^(-1(1)]=[-pi/2, pi/2]#.
Here, the Table with spacing
The axis of this semi sine wave is y-axis.
Now, you can make this half wave around y-axis, in the rectangle
Had we relaxed the principal value convention,
for successive periods
This happens for the inverse x = 2 sin y.