Find the exact value of each real number y if it exists. Do not use a calculator.

y = arccos (―√3/2)

Video transcript

Hello, everyone. We are asked to determine the exact value of the given inverse trigonometric function. Without using a calculator, we are given Y equals the arc cosine of negative radical. Two divided by two. Our answer choices are A Y equals negative pi divided by four by equals negative three pi divided by four cy equals three pi divided by four dy equals negative two pi divided by three. First. Since we are asked to do this without a calculator, we want to be able to reference a unit circle. If you do not have one, you should probably grab one. Now with that said, I wanna make sure that the value I'm looking at falls within the domain of the arc cosine function. So our domain here is between negative one and one including the end points and checking negative radical two divided by two does fit within our domain. So I know on my unit circle, I'm gonna look at the range and the range for the arc cosine is between zero and pi again including the end points. So on our coordinate plane zero to pi is quadrants one and two. So our answer will be in quadrant one or quadrant two, since I can rewrite Y equals the arc cosine of negative radical two divided by two as the cosine of Y equals negative radical two divided by two. And it's a negative I know we're going to be working in quadrant two because that's where cosine is negative. So looking on my unit circle in quadrant two, I find that to have a negative radical two divided by two, I am looking at the angle three pi divided by four. So why here is three pi divided by four and that's answer choice C have a nice day.