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Which graph shows the angle Ө = -210° in standard position?

Which graph shows the angle Ө = -210° in standard position?

Calculus: Early Transcendentals
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 consists of three diagrams, each displaying a circle with marked points and angles, oriented on a grid. The descriptions are as follows: 1. **Top Diagram:** - A circle is centered at point \( O \). - The circle is divided into four quadrants by the x-axis and y-axis. - An angle labeled \( 80^\circ \) is marked within the circle, with an arrow indicating its direction. - Angle \( \theta \) is marked at the origin and represents the angle formed with the positive x-axis. 2. **Middle Diagram:** - Similar to the top diagram, a circle is centered at \( O \) and divided into four quadrants by the x-axis and y-axis. - An angle marked \( 80^\circ \) is shown, but in this diagram, the arrow is directed along the negative x-axis. - Angle \( \theta \) is at the origin, measured from the positive y-axis, indicating a counter-clockwise direction. 3. **Bottom Diagram:** - Again, a circle is centered at \( O \) with the x-axis and y-axis creating quadrants. - The angle labeled \( 80^\circ \) has an arrow that completes a full counter-clockwise rotation starting from the negative y-axis. - Angle \( \theta \) indicates the sector's opening towards the negative x-axis. Each diagram demonstrates different orientations and directions of the same angle measurement, highlighting the concept of reference angles in standard position relative to the x and y axes.
Transcribed Image Text:The image consists of three diagrams, each displaying a circle with marked points and angles, oriented on a grid. The descriptions are as follows: 1. **Top Diagram:** - A circle is centered at point \( O \). - The circle is divided into four quadrants by the x-axis and y-axis. - An angle labeled \( 80^\circ \) is marked within the circle, with an arrow indicating its direction. - Angle \( \theta \) is marked at the origin and represents the angle formed with the positive x-axis. 2. **Middle Diagram:** - Similar to the top diagram, a circle is centered at \( O \) and divided into four quadrants by the x-axis and y-axis. - An angle marked \( 80^\circ \) is shown, but in this diagram, the arrow is directed along the negative x-axis. - Angle \( \theta \) is at the origin, measured from the positive y-axis, indicating a counter-clockwise direction. 3. **Bottom Diagram:** - Again, a circle is centered at \( O \) with the x-axis and y-axis creating quadrants. - The angle labeled \( 80^\circ \) has an arrow that completes a full counter-clockwise rotation starting from the negative y-axis. - Angle \( \theta \) indicates the sector's opening towards the negative x-axis. Each diagram demonstrates different orientations and directions of the same angle measurement, highlighting the concept of reference angles in standard position relative to the x and y axes.
## Question: Which graph shows the angle \( \theta = -210^\circ \) in standard position? ## Options: 1. **Graph 1:** - **Description:** This graph shows a circle with a marked central angle measuring \(30^\circ\) in the clockwise direction. The terminal side of the angle is positioned in the fourth quadrant. 2. **Graph 2:** - **Description:** This graph displays a circle with a central angle measuring \(210^\circ\) in the clockwise direction. The terminal side of this angle ends in the third quadrant. This represents the angle \(-210^\circ\). 3. **Graph 3:** - **Description:** This graph shows a circle with an angle labeled \( \theta \) in the clockwise direction. The angle appears to end in the third quadrant, similar to Graph 2, but the angle measure is not clearly marked. **Explanation:** - Negative angles are measured clockwise from the positive x-axis. - An angle of \(-210^\circ\) results in the terminal side being in the third quadrant. **Correct Answer: Graph 2** shows the angle \(\theta = -210^\circ\) in standard position.
Transcribed Image Text:## Question: Which graph shows the angle \( \theta = -210^\circ \) in standard position? ## Options: 1. **Graph 1:** - **Description:** This graph shows a circle with a marked central angle measuring \(30^\circ\) in the clockwise direction. The terminal side of the angle is positioned in the fourth quadrant. 2. **Graph 2:** - **Description:** This graph displays a circle with a central angle measuring \(210^\circ\) in the clockwise direction. The terminal side of this angle ends in the third quadrant. This represents the angle \(-210^\circ\). 3. **Graph 3:** - **Description:** This graph shows a circle with an angle labeled \( \theta \) in the clockwise direction. The angle appears to end in the third quadrant, similar to Graph 2, but the angle measure is not clearly marked. **Explanation:** - Negative angles are measured clockwise from the positive x-axis. - An angle of \(-210^\circ\) results in the terminal side being in the third quadrant. **Correct Answer: Graph 2** shows the angle \(\theta = -210^\circ\) in standard position.
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