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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
![### Question
If \(0 \leq \beta < 2\pi\), find all values of \(\beta\) that satisfy the equation
\[
\cos(2\beta) = \frac{\sqrt{3}}{2}
\]
Select the correct answer below:
- \( \beta = \frac{\pi}{12} \text{ and } \frac{11\pi}{12} \)
- \( \beta = \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{6}, \frac{4\pi}{3} \)
- \( \beta = \frac{\pi}{12}, \frac{11\pi}{12}, \frac{13\pi}{12}, \frac{23\pi}{12} \)
- \( \beta = \frac{\pi}{12}, \frac{\pi}{6}, \frac{7\pi}{12}, \frac{2\pi}{3}, \frac{13\pi}{12}, \frac{19\pi}{12}, \frac{5\pi}{3} \)
### Explanation
The values presented are possible solutions for \(\beta\) based on the cosine equation given. The problem requires us to identify which options correctly list all values of \(\beta\) within the given range that satisfy the equation \(\cos(2\beta) = \frac{\sqrt{3}}{2}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F109be86b-b006-4cdf-8d95-c931136e0133%2F61d8e255-0397-488b-9bd4-bc7e3ad6b58f%2Flmz9pxk.jpeg&w=3840&q=75)
Transcribed Image Text:### Question
If \(0 \leq \beta < 2\pi\), find all values of \(\beta\) that satisfy the equation
\[
\cos(2\beta) = \frac{\sqrt{3}}{2}
\]
Select the correct answer below:
- \( \beta = \frac{\pi}{12} \text{ and } \frac{11\pi}{12} \)
- \( \beta = \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{6}, \frac{4\pi}{3} \)
- \( \beta = \frac{\pi}{12}, \frac{11\pi}{12}, \frac{13\pi}{12}, \frac{23\pi}{12} \)
- \( \beta = \frac{\pi}{12}, \frac{\pi}{6}, \frac{7\pi}{12}, \frac{2\pi}{3}, \frac{13\pi}{12}, \frac{19\pi}{12}, \frac{5\pi}{3} \)
### Explanation
The values presented are possible solutions for \(\beta\) based on the cosine equation given. The problem requires us to identify which options correctly list all values of \(\beta\) within the given range that satisfy the equation \(\cos(2\beta) = \frac{\sqrt{3}}{2}\).
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