A What is a coterminal angle of 3π ? 4 B 7T 11T 4 4 international Academy of Science. All Rights Reserved. 4 C kl+
A What is a coterminal angle of 3π ? 4 B 7T 11T 4 4 international Academy of Science. All Rights Reserved. 4 C kl+
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
Hey what’s the answer to this
![**Understanding Coterminal Angles**
In this particular question, you are asked to determine a coterminal angle of \(\frac{3\pi}{4}\).
**Question**:
What is a coterminal angle of \(\frac{3\pi}{4}\)?
**Choices**:
A. \(-\frac{7\pi}{4}\)
B. \(\frac{11\pi}{4}\)
C. \(-\frac{\pi}{4}\)
**Explanation**:
Coterminal angles are angles that share the same initial and terminal sides. They can be found by adding or subtracting full rotations (360° or \(2\pi\) radians).
For example:
- To find a positive coterminal angle, add \(2\pi\) to \(\frac{3\pi}{4}\):
\[
\frac{3\pi}{4} + 2\pi = \frac{3\pi}{4} + \frac{8\pi}{4} = \frac{11\pi}{4}
\]
- To find a negative coterminal angle, subtract \(2\pi\) from \(\frac{3\pi}{4}\):
\[
\frac{3\pi}{4} - 2\pi = \frac{3\pi}{4} - \frac{8\pi}{4} = -\frac{5\pi}{4}
\]
Given these calculations, the options provided include one correct coterminal angle: B. \(\frac{11\pi}{4}\).
**Conclusion**:
Thus, the coterminal angle of \(\frac{3\pi}{4}\) from the options given is:
B. \(\frac{11\pi}{4}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59dc451e-d6f8-4dd4-9faf-549af2b24cc3%2F05233c63-b3b0-47c3-bdd8-3cc5821a27e1%2Fjb4fuh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Coterminal Angles**
In this particular question, you are asked to determine a coterminal angle of \(\frac{3\pi}{4}\).
**Question**:
What is a coterminal angle of \(\frac{3\pi}{4}\)?
**Choices**:
A. \(-\frac{7\pi}{4}\)
B. \(\frac{11\pi}{4}\)
C. \(-\frac{\pi}{4}\)
**Explanation**:
Coterminal angles are angles that share the same initial and terminal sides. They can be found by adding or subtracting full rotations (360° or \(2\pi\) radians).
For example:
- To find a positive coterminal angle, add \(2\pi\) to \(\frac{3\pi}{4}\):
\[
\frac{3\pi}{4} + 2\pi = \frac{3\pi}{4} + \frac{8\pi}{4} = \frac{11\pi}{4}
\]
- To find a negative coterminal angle, subtract \(2\pi\) from \(\frac{3\pi}{4}\):
\[
\frac{3\pi}{4} - 2\pi = \frac{3\pi}{4} - \frac{8\pi}{4} = -\frac{5\pi}{4}
\]
Given these calculations, the options provided include one correct coterminal angle: B. \(\frac{11\pi}{4}\).
**Conclusion**:
Thus, the coterminal angle of \(\frac{3\pi}{4}\) from the options given is:
B. \(\frac{11\pi}{4}\)
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