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

Question

contestada

Respuesta :

RushdaE335241 RushdaE335241 · Answer 1 · 2022-10-30T16:39:27+01:00

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

[tex]-\frac{\pi}{2}\le x\le\frac{\pi}{2}[/tex]

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

[tex]\begin{gathered} \text{Range of the sine inverse function:} \\ -\frac{\pi}{2}\le y\le\frac{\pi}{2} \end{gathered}[/tex]

which corresponds to the interval:

[tex]\lbrack-\frac{\pi}{2},\frac{\pi}{2}\rbrack\text{ In quadrants I and IV}[/tex]