Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Identifying Coterminal Angles
#### Problem Statement:
An angle measures \(150^\circ\). Which of the following is **not** a coterminal angle measure?
1. \( -210^\circ \)
2. \( 510^\circ \)
3. \( \frac{\pi}{6} \)
4. \( \frac{5\pi}{6} \)
#### Explanation of Coterminal Angles:
Coterminal angles are angles that, when drawn in standard position (having the initial side along the positive x-axis), share the same terminal side. These angles differ by an integer multiple of \(360^\circ\), or \(2\pi\) radians.
To find out if two angles are coterminal, you can periodically add or subtract \(360^\circ\) (or \(2\pi\) radians) until you get into the standard \(0^\circ\) to \(360^\circ\) range.
#### Option Analysis:
1. **For \( -210^\circ \)**:
Adding \(360^\circ\) to \( -210^\circ \):
\[
-210^\circ + 360^\circ = 150^\circ
\]
Hence, \(-210^\circ\) is coterminal with \(150^\circ\).
2. **For \( 510^\circ \)**:
Subtracting \(360^\circ\) from \(510^\circ\):
\[
510^\circ - 360^\circ = 150^\circ
\]
Therefore, \(510^\circ\) is coterminal with \(150^\circ\).
3. **For \( \frac{\pi}{6} \)**:
Converting radians to degrees:
\[
\frac{\pi}{6} \times \frac{180^\circ}{\pi} = 30^\circ
\]
Since \(30^\circ\) is not coterminal with \(150^\circ\), \(\frac{\pi}{6}\) is not a coterminal angle.
4. **For \( \frac{5\pi}{6} \)**:
Converting radians to degrees:
\[
\frac{5\pi}{6} \times \frac{180^\circ}{\pi} = 150^\circ
\]
Therefore, \(\frac{5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf693007-feb9-4e65-ba86-b1b16e800487%2F96d817f7-0fc4-42d9-a219-9a9521509a91%2F6omzbn_processed.png&w=3840&q=75)
Transcribed Image Text:### Identifying Coterminal Angles
#### Problem Statement:
An angle measures \(150^\circ\). Which of the following is **not** a coterminal angle measure?
1. \( -210^\circ \)
2. \( 510^\circ \)
3. \( \frac{\pi}{6} \)
4. \( \frac{5\pi}{6} \)
#### Explanation of Coterminal Angles:
Coterminal angles are angles that, when drawn in standard position (having the initial side along the positive x-axis), share the same terminal side. These angles differ by an integer multiple of \(360^\circ\), or \(2\pi\) radians.
To find out if two angles are coterminal, you can periodically add or subtract \(360^\circ\) (or \(2\pi\) radians) until you get into the standard \(0^\circ\) to \(360^\circ\) range.
#### Option Analysis:
1. **For \( -210^\circ \)**:
Adding \(360^\circ\) to \( -210^\circ \):
\[
-210^\circ + 360^\circ = 150^\circ
\]
Hence, \(-210^\circ\) is coterminal with \(150^\circ\).
2. **For \( 510^\circ \)**:
Subtracting \(360^\circ\) from \(510^\circ\):
\[
510^\circ - 360^\circ = 150^\circ
\]
Therefore, \(510^\circ\) is coterminal with \(150^\circ\).
3. **For \( \frac{\pi}{6} \)**:
Converting radians to degrees:
\[
\frac{\pi}{6} \times \frac{180^\circ}{\pi} = 30^\circ
\]
Since \(30^\circ\) is not coterminal with \(150^\circ\), \(\frac{\pi}{6}\) is not a coterminal angle.
4. **For \( \frac{5\pi}{6} \)**:
Converting radians to degrees:
\[
\frac{5\pi}{6} \times \frac{180^\circ}{\pi} = 150^\circ
\]
Therefore, \(\frac{5
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