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

In this problem, we're asked to identify what quadrant the given angle is in and here we're given the angle in radians pi over 7 radians. Now we're going to use 2 things here, our knowledge and the angles that we already know on our unit circle, so let's go ahead and get started. Now looking at this angle pi over 7, if I consider all of the angles that I know on my unit circle, I know that I start at 0 and then I rotate around to my 1st quadrantal angle, the one that is directly in between quadrant 1 and quadrant 2, and this angle is pi over 2. Now whenever I have a fraction, if my denominator is larger than some other fraction and they have the same exact numerator, I know that that angle has to be smaller. So this pi over 2, since this has a denominator of 2 and my given angle has a denominator of 7 and they both have that numerator of pi, I know that pi over 7 is less than pi over 2. So that tells me that my angle sits in between 0 and pi over 2 on my unit circle. So it is right here in quadrant 1. So pi over 7 radians is an angle that is in quadrant 1 of my unit circle. 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.
$\frac{\pi}{7}$ radians

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Verified step by step guidance

Convert the given angle from radians to degrees to make it easier to understand. Use the conversion formula: degrees = radians × (180/π).

Calculate the degree measure of the angle: (π/7) × (180/π) = 180/7 degrees.

Simplify the expression to find the degree measure: 180/7 degrees is approximately 25.71 degrees.

Recall the quadrant system: Quadrant I is from 0 to 90 degrees, Quadrant II is from 90 to 180 degrees, Quadrant III is from 180 to 270 degrees, and Quadrant IV is from 270 to 360 degrees.

Determine which quadrant the angle falls into: Since 25.71 degrees is between 0 and 90 degrees, the angle is located in Quadrant I.

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Struggling with Trigonometry?

Identify the quadrant that the given angle is located in.π7\(\frac{\pi}{7}\)7π radians

Watch next

Defining the Unit Circle practice set

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