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67 - The angles is drawn in standard position. In what quadrant will the terminal side of the angle lie?

67 - The angles is drawn in standard position. In what quadrant will the terminal side of the angle lie?

Trigonometry (11th Edition)
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:** The angle \(\frac{6\pi}{5}\) is drawn in standard position. In what quadrant will the terminal side of the angle lie? **Diagram:** The provided diagram is a coordinate plane divided into four quadrants: - **Quadrant I** is in the upper right. - **Quadrant II** is in the upper left. - **Quadrant III** is in the bottom left. - **Quadrant IV** is in the bottom right. Since \(\frac{6\pi}{5}\) is greater than \(\pi\) (which is \(5\pi/5\)) and less than \(2\pi\) (which is \(10\pi/5\)), the terminal side of the angle lies in Quadrant III. **Options:** - A. IV - B. I - C. III - D. II Correct answer: **C. III** **Explanation:** When an angle measured in radians is between \(\pi\) and \(3\pi/2\) (or equivalently, between \(5\pi/5\) and \(7.5\pi/5\)), its terminal side will lie in Quadrant III. Given \(\frac{6\pi}{5}\) falls into this interval, the terminal side of the angle will indeed be in Quadrant III. **Interface Note:** Below the diagram, there is a multiple-choice selection with four options and a progress tracker indicating the 5th of 15 questions has been answered. The interface shows options to "Continue" to the next question.
Transcribed Image Text:**Question:** The angle \(\frac{6\pi}{5}\) is drawn in standard position. In what quadrant will the terminal side of the angle lie? **Diagram:** The provided diagram is a coordinate plane divided into four quadrants: - **Quadrant I** is in the upper right. - **Quadrant II** is in the upper left. - **Quadrant III** is in the bottom left. - **Quadrant IV** is in the bottom right. Since \(\frac{6\pi}{5}\) is greater than \(\pi\) (which is \(5\pi/5\)) and less than \(2\pi\) (which is \(10\pi/5\)), the terminal side of the angle lies in Quadrant III. **Options:** - A. IV - B. I - C. III - D. II Correct answer: **C. III** **Explanation:** When an angle measured in radians is between \(\pi\) and \(3\pi/2\) (or equivalently, between \(5\pi/5\) and \(7.5\pi/5\)), its terminal side will lie in Quadrant III. Given \(\frac{6\pi}{5}\) falls into this interval, the terminal side of the angle will indeed be in Quadrant III. **Interface Note:** Below the diagram, there is a multiple-choice selection with four options and a progress tracker indicating the 5th of 15 questions has been answered. The interface shows options to "Continue" to the next question.
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