Hey, everyone. In this problem, we're asked to evaluate the expression the inverse cosine of negative square root of 3 over 2. Now whenever working with an inverse trigonometric function, remember that we can also think of this as: Okay, the cosine of what angle is equal to negative square root of 3 over 2, and we want to find the angle for which that is true.

Now when working with the inverse cosine, we know that our angles can only be between 0 and pi. But we can actually get even more specific here because we know that all of our cosine values are going to be positive in quadrant 1 and all of our cosine values in quadrant 2 are going to be negative. So, whenever we're taking the inverse cosine of a positive number, we know that our solution has to be in quadrant 1. And whenever we're taking the inverse cosine of a negative number, just like we are here, we know that our solution has to be in quadrant 2.

Here, we already know that our angle has to be in this second quadrant. So, for which one of these angles is the cosine equal to negative square root of 3 over 2? Well, I know that the cosine of 5 pi over 6 is equal to just that, so that represents my solution. My angle here is 5 6 π and we are done here. Thanks for watching, and I'll see you in the next one.