Sec 6.6 Inverse Trig: Probien 3
(1 point)
Find the domain and the range of ,
Domain:
Range:
Note: You can earn partial credit on this problem.

To determine the domain of , we need to ensure that the argument of the inverse sine function, , falls within the valid output of the sine function, which is between -1 and 1. Therefore, we set up the inequalities:

Solving these, we get:

So the domain is:

Next, for the range, since the output of the function where takes values from the domain, we know the range of the inverse sine function is between and :

Putting it all together, the answers are:
Domain:
Range: