Hey everyone. In this problem, we're asked to evaluate the expression the inverse cosine of negative 32. Now whenever working with an inverse trig function, remember that we can also think of this as, "Okay, the cosine of what angle is equal to negative 32?" And we want to find the angle for which that is true. Now when working with the inverse cosine, we know that our values, our angles, can only be between 0 and π.
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. So here we already know that our angle has to be in the second quadrant. So for which one of these angles is the cosine equal to negative 32?
Well, I know that the cosine of 5π over 6 is equal to just that so that represents my solution. My angle here is 5π over 6 and we are done here. Thanks for watching, and I'll see you in the next one.