Hey everyone. In this problem, we're asked to evaluate the expression the inverse sine of negative one. Now, remember when working with inverse trig functions, we can also think of this as "the sine of what angle is equal to negative one," and we're looking for the angle for which that is true. Now when working with the inverse sine specifically, we know that our solution can only be angles between negative pi over 2 and positive pi over 2, but we can get even more specific here because all of my sine values in this first quadrant, quadrant 1, from 0 to pi over 2, are going to be positive. Whereas in the 4th quadrant, from negative pi over 2 to 0, all of these sine values are going to be negative.
So if I'm taking the inverse sine of a positive value, I know that my solution has to be in quadrant 1. Whereas if I'm taking the inverse sine of a negative value, like we are here, the inverse sine of negative one, we know that our solution has to be in quadrant 4 between negative pi over 2 and 0. So here, since we're taking the inverse sine of negative one, I already know that my solution has to be down here in this 4th quadrant. So, where is the sine equal to negative one? Well, for negative pi over 2, I know that my sine, or my y-value, is equal to negative one.
So here my angle, and my solution to this expression is negative pi over 2, and we are done here. Thanks for watching and I'll see you in the next one.
