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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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Question
**Title: Understanding the Unit Circle** *Draw the angle \(\frac{\pi}{3}\).* **Diagram Explanation:** The diagram illustrates a unit circle (a circle with a radius of 1), centered at the origin of a coordinate system. The circle is depicted with the following details: - **Axes and Grid**: A Cartesian coordinate system is used, with both the x-axis and y-axis marked with intervals of 0.2, ranging from -1.4 to 1.4. - **Unit Circle**: The circle intersects the x-axis at (1, 0) and (-1, 0), and the y-axis at (0, 1) and (0, -1). - **Circle Points**: The circle is marked with small dots indicating points on its circumference. - **Angle Representation**: Although not explicitly shown in the diagram with a ray or line, the task is to draw the angle \(\frac{\pi}{3}\), which corresponds to approximately 60 degrees. - **Quadrants**: The circle is divided into four equal parts by the axes: Quadrants I, II, III, and IV. **Educational Context:** The unit circle is a fundamental concept in trigonometry, often used to define trigonometric functions for angles. Angles measured in radians, such as \(\frac{\pi}{3}\), are critical in various math and engineering applications. In this context, the angle \(\frac{\pi}{3}\) would typically be drawn starting from the positive x-axis (0 radians), moving counterclockwise to reach a point on the circle in the first quadrant.
Transcribed Image Text:**Title: Understanding the Unit Circle** *Draw the angle \(\frac{\pi}{3}\).* **Diagram Explanation:** The diagram illustrates a unit circle (a circle with a radius of 1), centered at the origin of a coordinate system. The circle is depicted with the following details: - **Axes and Grid**: A Cartesian coordinate system is used, with both the x-axis and y-axis marked with intervals of 0.2, ranging from -1.4 to 1.4. - **Unit Circle**: The circle intersects the x-axis at (1, 0) and (-1, 0), and the y-axis at (0, 1) and (0, -1). - **Circle Points**: The circle is marked with small dots indicating points on its circumference. - **Angle Representation**: Although not explicitly shown in the diagram with a ray or line, the task is to draw the angle \(\frac{\pi}{3}\), which corresponds to approximately 60 degrees. - **Quadrants**: The circle is divided into four equal parts by the axes: Quadrants I, II, III, and IV. **Educational Context:** The unit circle is a fundamental concept in trigonometry, often used to define trigonometric functions for angles. Angles measured in radians, such as \(\frac{\pi}{3}\), are critical in various math and engineering applications. In this context, the angle \(\frac{\pi}{3}\) would typically be drawn starting from the positive x-axis (0 radians), moving counterclockwise to reach a point on the circle in the first quadrant.
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