Identify the quadrant that the given angle is located in. 2 π 3 \frac{2\pi}{3} 3 2 π radians

In this problem, we're asked to identify what quadrant of our unit circle our given angle is in and the angle we're given here is in radians. It's 2 pi over 3 radians. Now again, here we're going to use our knowledge of fractions and those angles that we already know on our unit circles. So looking at this angle, 2 pi over 3. Something that might be helpful to you when looking at problems specifically like this is to ignore that pi in your radian angle measure. Now you shouldn't do this all the time, but whenever we're just looking at where our angle fits into our unit circle, this might be helpful because you might be more familiar with fractions when you don't have to worry about that pie. So here, if we consider this angle or this fraction to be 2 thirds and we look at our unit circle and we see that we start with fraction to be 2 thirds and we look at our unit circle and we see that we start with 0 and ignoring this pie here, this is really a fraction of 1 half. And then here with this pie, this is a fraction of 1. Now when we consider where 2 thirds fits into that, I know that 2 thirds fraction of 1. Now when we consider where 2 thirds fits into that, I know that 2 thirds is less than 1, so I know that it has to be either in quadrant 1 or quadrant 2. Now when I consider its relation to 1 half, 2 thirds is a fraction that is definitely larger than 1 half. So I know that 2 thirds is greater than 1 half, which also tells me that 2 pi over 3 is greater than pi over 2. So that tells me that this fraction, this angle, sits right in between my fraction of pi over 2 and pi right in quadrant 2. So this angle, 2 pi over 3 radians, is in quadrant 2. Thanks for watching, and let me know if you have questions.

3. Unit Circle

Defining the Unit Circle

Trigonometry

3. Unit Circle

Defining the Unit Circle

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Multiple Choice

Identify the quadrant that the given angle is located in.
$\frac{2\pi}{3}$ radians

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Verified step by step guidance

Convert the given angle from radians to degrees if necessary. However, in this case, we will work directly with radians.

Recall that the unit circle is divided into four quadrants: Quadrant I (0 to π/2), Quadrant II (π/2 to π), Quadrant III (π to 3π/2), and Quadrant IV (3π/2 to 2π).

The given angle is $ \frac{2\pi}{3} $ radians. Determine which interval this angle falls into by comparing it with the boundaries of each quadrant.

Since $ \frac{2\pi}{3} $ is greater than $ \frac{\pi}{2} $ and less than $ \pi $, it falls within the range of Quadrant II.

Conclude that the angle $ \frac{2\pi}{3} $ radians is located in Quadrant II.

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Struggling with Trigonometry?

Identify the quadrant that the given angle is located in.2π3\frac{2\pi}{3}32π radians

Watch next

Defining the Unit Circle practice set

Identify the quadrant that the given angle is located in.
$\frac{2\pi}{3}$ radians