Identify the quadrant that the given angle is located in. 7 π 4 \frac{7\pi}{4} radians

Hey everyone. In this problem, we're asked to identify the quadrant that the given angle is located in. And the angle that we're given is in radians. It's 7 pi over 4 radians. Now looking at this problem, you can choose to convert this radian angle measure into degrees if that makes it more simple for you. But here, I'm going to walk you through how to identify where this angle is located using exclusively its radian measure just so that we get a little bit more familiar with radians along the way. So let's go ahead and get started. Now looking at this angle 7 pi over 4, the first thing that I notice is that that numerator 7 pi is larger than my denominator of 4. So I know that this angle is going to be greater than 1 or in this case, we can look at it in relation to pi. This is going to be an angle that is a greater than pi. So I know that this has to be located either in quadrant 3 or quadrant 4 because looking at my unit circle starting from 0 going around, here is pi, so I know that it has to be in that bottom in those bottom two quadrants. So now we need to look at its relation to this other angle, 3 pi over 2. If it is a fraction that is smaller than 3 pi over 2, I know that it will be located in quadrant 3. Whereas if it's greater than 3 pi over 2, I know that it will be located in quadrant 4. So let's determine that. Now looking at this fraction 3 pi over 2, it can be really helpful to give this the same denominator as our given angle 7 pi over 4. So let's go ahead and do that. Now if I multiply 3 pi over 2 by 2 over 2, keeping it the same exact number but just altering that denominator, This gives me 6 pi over 4. Now when looking at 7pi over 4 and 6pi over 4, it makes it much easier to tell which one is greater. 7pi over 4 has a greater numerator with the same denominator, so I know that it is a greater angle than 6pi over 4. Now because of that, that tells me that my angle will be located to the right of this going clock counterclockwise around my circle. So that tells me that 7 pi over 4 radians is an angle located in that last quadrant, quadrant 4. Thanks for watching, and let me know if you have questions.

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Multiple Choice

Identify the quadrant that the given angle is located in.
$7 pi over 4$ radians

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

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Identify the quadrant that the given angle is located in.7π4\(\frac{7\pi}{4}\) radians

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Identify the quadrant that the given angle is located in.
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