The angle between 0° and 360° that is coterminal with the 688° angle is degrees.
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°.
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Question
![**Coterminal Angles Explanation**
**Problem Statement:**
The angle between \(0^\circ\) and \(360^\circ\) that is coterminal with the \(688^\circ\) angle is _____ degrees.
**Solution:**
Coterminal angles are angles that share the same initial and terminal sides but may differ by an integer multiple of a full rotation (360°). To find a coterminal angle between 0° and 360° for an angle given in degrees, follow these steps:
1. **Determine the equivalent angle** by subtracting 360° from the given angle until the result is within the desired range (0° to 360°).
\[
688^\circ - 360^\circ = 328^\circ
\]
Since \(328^\circ\) is between 0° and 360°, it is the coterminal angle within this range.
**Answer:**
The angle between \(0^\circ\) and \(360^\circ\) that is coterminal with the \(688^\circ\) angle is \(328^\circ\).
**Educational Insight:**
Understanding coterminal angles is crucial in various fields of mathematics, particularly in trigonometry and geometry. It helps in simplifying the study of periodic functions and rotational movements by providing a standard range for angle measurements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F762dd5f9-d116-4be3-9bac-36a96db639f5%2Fbe8ccd3e-4c27-4c28-a838-35a472b01786%2Fdq980y9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Coterminal Angles Explanation**
**Problem Statement:**
The angle between \(0^\circ\) and \(360^\circ\) that is coterminal with the \(688^\circ\) angle is _____ degrees.
**Solution:**
Coterminal angles are angles that share the same initial and terminal sides but may differ by an integer multiple of a full rotation (360°). To find a coterminal angle between 0° and 360° for an angle given in degrees, follow these steps:
1. **Determine the equivalent angle** by subtracting 360° from the given angle until the result is within the desired range (0° to 360°).
\[
688^\circ - 360^\circ = 328^\circ
\]
Since \(328^\circ\) is between 0° and 360°, it is the coterminal angle within this range.
**Answer:**
The angle between \(0^\circ\) and \(360^\circ\) that is coterminal with the \(688^\circ\) angle is \(328^\circ\).
**Educational Insight:**
Understanding coterminal angles is crucial in various fields of mathematics, particularly in trigonometry and geometry. It helps in simplifying the study of periodic functions and rotational movements by providing a standard range for angle measurements.
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