Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Determining Coterminal Angles
**Instructions:**
Determine the angle between \( 0 \) and \( 2\pi \) that is coterminal to \( 1020^\circ \).
**Answer Choices:**
- \( \frac{10\pi}{3} \)
- \( \frac{5\pi}{3} \)
- \( \frac{4\pi}{3} \)
- \( \frac{\pi}{3} \)
**Explanation:**
To find the angle coterminal to \( 1020^\circ \), we can use the property that coterminal angles differ by multiples of \( 360^\circ \). We need to find an equivalent angle between \( 0^\circ \) and \( 360^\circ \).
### Steps:
1. Subtract \( 360^\circ \) from \( 1020^\circ \) repeatedly until the result is between \( 0^\circ \) and \( 360^\circ \):
- \( 1020^\circ - 360^\circ = 660^\circ \)
- \( 660^\circ - 360^\circ = 300^\circ \)
Hence, \( 1020^\circ \) is coterminal with \( 300^\circ \).
2. Convert \( 300^\circ \) to radians:
\[ 300^\circ \times \frac{\pi}{180^\circ} = \frac{5\pi}{3} \]
Therefore, the angle in radians between \( 0 \) and \( 2\pi \) that is coterminal to \( 1020^\circ \) is \( \frac{5\pi}{3} \).
So, the correct answer is:
\[ \textbf{\(\ \frac{5\pi}{3}\ \)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e08c0ed-2478-4250-8ecc-80933702ca06%2F7481be56-47cb-4ac5-8b75-15c02034ae2b%2F7qigg0m_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining Coterminal Angles
**Instructions:**
Determine the angle between \( 0 \) and \( 2\pi \) that is coterminal to \( 1020^\circ \).
**Answer Choices:**
- \( \frac{10\pi}{3} \)
- \( \frac{5\pi}{3} \)
- \( \frac{4\pi}{3} \)
- \( \frac{\pi}{3} \)
**Explanation:**
To find the angle coterminal to \( 1020^\circ \), we can use the property that coterminal angles differ by multiples of \( 360^\circ \). We need to find an equivalent angle between \( 0^\circ \) and \( 360^\circ \).
### Steps:
1. Subtract \( 360^\circ \) from \( 1020^\circ \) repeatedly until the result is between \( 0^\circ \) and \( 360^\circ \):
- \( 1020^\circ - 360^\circ = 660^\circ \)
- \( 660^\circ - 360^\circ = 300^\circ \)
Hence, \( 1020^\circ \) is coterminal with \( 300^\circ \).
2. Convert \( 300^\circ \) to radians:
\[ 300^\circ \times \frac{\pi}{180^\circ} = \frac{5\pi}{3} \]
Therefore, the angle in radians between \( 0 \) and \( 2\pi \) that is coterminal to \( 1020^\circ \) is \( \frac{5\pi}{3} \).
So, the correct answer is:
\[ \textbf{\(\ \frac{5\pi}{3}\ \)} \]
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