The arcsin function or `sin^-1` is the inverse to the sine function. Since only there can only be one value of y for each value of x for it to be a function, arcsin can only be defined in an interval.

Plot values of x, sin x and `sin^-1x` or asin x

x y= sin x asin y

0 0 0

`pi/4` `1/sqrt2` `pi/4`

`pi/2` 1 `pi/2`

`3pi/4` `1/sqrt2` Thus this point is undefined for arcsin because it would have the same value.

`-pi/2` `-1` `-pi/2`

The inverse function of y=sinx is y=arcsinx, thus the plot values are

x y= arcsin x

0 0

`1/sqrt2` `pi/4`

1 `pi/2`

`-1/sqrt2` `-pi/4`

-1 `-pi/2`

And `-pi/2<=x<=pi/2`