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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![The image contains a multiple-choice math problem asking to determine the angle between \(0\) and \(2\pi\) that is coterminal with \(\frac{19\pi}{4}\). Below the question, there are four answer choices, each formatted as a fraction involving \(\pi\).
**Question:**
Determine the angle between \(0\) and \(2\pi\) that is coterminal with \(\frac{19\pi}{4}\).
**Answer Choices:**
1. \(\frac{11\pi}{4}\)
2. \(\frac{5\pi}{4}\)
3. \(\frac{3\pi}{4}\)
4. \(\frac{\pi}{4}\)
Explanation:
A coterminal angle is an angle that differs from a given angle by a multiple of \(2\pi\). To find an angle that is coterminal with \(\frac{19\pi}{4}\) and lies between \(0\) and \(2\pi\), we can subtract \(2\pi\) multiples from \(\frac{19\pi}{4}\) until the angle lies within the desired range.
\[
\frac{19\pi}{4} - 2\pi \times 2 = \frac{19\pi}{4} - \frac{16\pi}{4} = \frac{3\pi}{4}
\]
Thus, the angle between \(0\) and \(2\pi\) that is coterminal with \(\frac{19\pi}{4}\) is \(\frac{3\pi}{4}\).
Therefore, the correct answer is:
- \(\frac{3\pi}{4}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3047b756-b2f4-4f66-ba10-7c0773ac07fd%2Fa5512d5e-d6b9-400f-a882-dd6564d468b3%2Fwuws69g_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains a multiple-choice math problem asking to determine the angle between \(0\) and \(2\pi\) that is coterminal with \(\frac{19\pi}{4}\). Below the question, there are four answer choices, each formatted as a fraction involving \(\pi\).
**Question:**
Determine the angle between \(0\) and \(2\pi\) that is coterminal with \(\frac{19\pi}{4}\).
**Answer Choices:**
1. \(\frac{11\pi}{4}\)
2. \(\frac{5\pi}{4}\)
3. \(\frac{3\pi}{4}\)
4. \(\frac{\pi}{4}\)
Explanation:
A coterminal angle is an angle that differs from a given angle by a multiple of \(2\pi\). To find an angle that is coterminal with \(\frac{19\pi}{4}\) and lies between \(0\) and \(2\pi\), we can subtract \(2\pi\) multiples from \(\frac{19\pi}{4}\) until the angle lies within the desired range.
\[
\frac{19\pi}{4} - 2\pi \times 2 = \frac{19\pi}{4} - \frac{16\pi}{4} = \frac{3\pi}{4}
\]
Thus, the angle between \(0\) and \(2\pi\) that is coterminal with \(\frac{19\pi}{4}\) is \(\frac{3\pi}{4}\).
Therefore, the correct answer is:
- \(\frac{3\pi}{4}\)
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