The range of the provided inverse sine function in terms of x, and y y = sin-1x is [-π/2, π/2].
Range of a function is the set of all the possible output values which are valid for that function.
The trigonometry function given in the problem is,
[tex]y = \sin^{-1}x[/tex]
The above function can be written as,
[tex]\sin y = x[/tex]
The above function is the arc of sine function. The domain of arc of sine ranges from -1 to 1.
[tex]-1\leq x\leq1[/tex]
This is the domain of the inverse of sine function. In the attached image below, the graph of inverse sine function is plotted. The range of this function is,
[tex]-\dfrac{\pi}{2}\leq x\leq\dfrac{\pi}{2}[/tex]
Thus, the range of the provided inverse sine function in terms of x, and y y = sin-1x is [-π/2, π/2].
Learn more about the range of the function here;
https://brainly.com/question/2264373
