Question

Find the range rule for the inverse function y=sin^-1(x). here are my answer options:Interval [1,-1] in quadrants 1 and 4Interval (-pi/2, pi/2) in quadrants I and IIIInterval [0,pi] in quadrants I and IIinterval [-pi/2, pi/2] in quadrants I and IV

Answer 1

The domain of Sine function (sin(x)) is given by

`-(\pi)/(2)\le x\le(\pi)/(2)`

since the domain of a function is the range of its inverse, therefore, the answer is:

`\begin{gathered} \text{Range of the sine inverse function:} \\ -(\pi)/(2)\le y\le(\pi)/(2) \end{gathered}`

which corresponds to the interval:

`\lbrack-(\pi)/(2),(\pi)/(2)\rbrack\text{ In quadrants I and IV}`