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.

Table of contents

Skip topic navigation

0. Fundamental Concepts of Algebra3h 32m
1. Equations and Inequalities3h 27m
2. Graphs1h 43m
3. Functions & Graphs2h 17m
4. Polynomial Functions1h 54m
5. Rational Functions1h 23m
6. Exponential and Logarithmic Functions2h 28m
7. Measuring Angles40m
8. Trigonometric Functions on Right Triangles2h 5m
9. Unit Circle1h 19m
10. Graphing Trigonometric Functions1h 19m
11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
12. Trigonometric Identities 2h 34m
13. Non-Right Triangles1h 38m
14. Vectors2h 25m
15. Polar Equations2h 5m
16. Parametric Equations1h 6m
17. Graphing Complex Numbers1h 7m
18. Systems of Equations and Matrices3h 6m
19. Conic Sections2h 36m
20. Sequences, Series & Induction1h 15m
21. Combinatorics and Probability1h 45m
22. Limits & Continuity1h 49m
23. Intro to Derivatives & Area Under the Curve2h 9m

9. Unit Circle

Defining the Unit Circle

Precalculus

9. Unit Circle

Defining the Unit Circle

Previous problemNext problem

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

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

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Previous problemNext problem

Verified step by step guidance

Convert the given angle from radians to degrees if necessary, but 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).

Determine the approximate value of the given angle in terms of π. Here, 7π/7 simplifies to π, which is exactly on the boundary between Quadrant II and Quadrant III.

Since the angle π is exactly on the boundary, it is typically considered to be in Quadrant II for the purpose of this problem.

Conclude that the angle π/7 is less than π/2, placing it in Quadrant I.