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 two pi over three 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, two pi over three. 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 two thirds and we look at our unit circle and we see that we start with zero and ignoring this pie here, this is really a fraction of one half. And then here with this pi, this is a fraction of one. Now when we consider where two thirds fits into that, I know that two thirds is less than one, so I know that it has to be either in quadrant one or quadrant two. Now when I consider its relation to one half, two thirds is a fraction that is definitely larger than one half. So I know that two thirds is greater than one half, which also tells me that two pi over three is greater than pi over two. So that tells me that this fraction, this angle, sits right in between my fraction of pi over two and pi right in quadrant two. So this angle, two pi over three radians, is in quadrant two. Thanks for watching, and let me know if you have questions.

12. Trigonometric Functions

Trigonometric Functions on the Unit Circle

Business Calculus

12. Trigonometric Functions

Trigonometric Functions on 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 $ \frac{2\pi}{3} $ radians into degrees for easier interpretation, if necessary. Use the conversion formula: $ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} $.

Recognize that $ \frac{2\pi}{3} $ radians is already in terms of $ \pi $, so it represents an angle between 0 and $ \pi $ radians (since $ \pi $ radians equals 180 degrees).

Determine the approximate value of $ \frac{2\pi}{3} $ radians in degrees. Using the conversion, $ \frac{2\pi}{3} $ radians equals approximately 120 degrees.

Identify the quadrant by analyzing the angle's position. Angles between 90 degrees and 180 degrees (or $ \frac{\pi}{2} $ and $ \pi $ radians) are located in Quadrant II.

Conclude that the given angle $ \frac{2\pi}{3} $ radians is located in Quadrant II based on its value and position on the unit circle.

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

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Trigonometric Functions on the Unit Circle practice set

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