How to find the graph of y=arcsin(x)

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flbyrne | (Level 3) Assistant Educator

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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`