Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Task 1. Building f(x) = sin(x)** Using the Unit Circle that we built before, put the values of sin(x) for each angle below. Then see each point plotted in the graph. Compare the behavior of the graph with your answer about the change in y-coordinate from the Warm Up. **Graph Explanation:** The graph on the left has the y-axis labeled as "sin(x)" ranging from -2 to 2. The x-axis is labeled as "x (degrees)" ranging from 0 to 360 degrees, marked in increments of 30 degrees. You will plot the sine values for each corresponding angle from the table provided. **Table:** | x (degrees) | Sin(x) | |-------------|------------------| | 0 | | | 30 | | | 45 | | | 60 | | | 90 | | | 120 | | | 135 | | | 150 | | | 180 | | | 210 | | | 225 | | | 240 | | | 270 | | | 300 | | | 315 | | | 330 | | | 360 | |
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Transcribed Image Text:**Task 1. Building f(x) = sin(x)** Using the Unit Circle that we built before, put the values of sin(x) for each angle below. Then see each point plotted in the graph. Compare the behavior of the graph with your answer about the change in y-coordinate from the Warm Up. **Graph Explanation:** The graph on the left has the y-axis labeled as "sin(x)" ranging from -2 to 2. The x-axis is labeled as "x (degrees)" ranging from 0 to 360 degrees, marked in increments of 30 degrees. You will plot the sine values for each corresponding angle from the table provided. **Table:** | x (degrees) | Sin(x) | |-------------|------------------| | 0 | | | 30 | | | 45 | | | 60 | | | 90 | | | 120 | | | 135 | | | 150 | | | 180 | | | 210 | | | 225 | | | 240 | | | 270 | | | 300 | | | 315 | | | 330 | | | 360 | |
**Educational Website Content: Understanding the Sine Function** **Introduction:** The sine function, represented as sin(x), is fundamental in trigonometry and has applications in various fields such as physics, engineering, and computer science. It describes a smooth, periodic oscillation. **Graph Explanation:** The image displays a graph and a table related to the sine function. 1. **Graph:** - The graph on the left shows the sine function plotted against angles ranging from 0 to 360 degrees. - The x-axis represents the angle in degrees. - The y-axis, ranging from -2 to 2, represents the sine values. - The sine curve is periodic and oscillates between -1 and 1. 2. **Table:** - The table on the right is meant to record the values of sin(x) for various angles x. - The first column lists angle values in degrees: 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360° - The second column is for the corresponding sine values to be filled in for each angle. **Data Entry:** To complete the table: - Use the sine function on a calculator or mathematical software to find the sine values for the given angles. - For example: - Sin(0°) = 0 - Sin(30°) = 0.5 - Sin(45°) = √2/2 ≈ 0.707 - Continue this process for all listed angles. **Interactive Component:** - An input box labeled "Submit" is provided below the table for entering and submitting the calculated sine values. **Conclusion:** Understanding the sine function and its values for different angles is crucial for further studies in trigonometry and its applications. Once you've filled in the table, you'll have a clearer picture of how the sine function behaves. **Note:** Errors in sine value calculation can lead to misunderstandings in subsequent applications, so double-check your values for accuracy.
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Transcribed Image Text:**Educational Website Content: Understanding the Sine Function** **Introduction:** The sine function, represented as sin(x), is fundamental in trigonometry and has applications in various fields such as physics, engineering, and computer science. It describes a smooth, periodic oscillation. **Graph Explanation:** The image displays a graph and a table related to the sine function. 1. **Graph:** - The graph on the left shows the sine function plotted against angles ranging from 0 to 360 degrees. - The x-axis represents the angle in degrees. - The y-axis, ranging from -2 to 2, represents the sine values. - The sine curve is periodic and oscillates between -1 and 1. 2. **Table:** - The table on the right is meant to record the values of sin(x) for various angles x. - The first column lists angle values in degrees: 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360° - The second column is for the corresponding sine values to be filled in for each angle. **Data Entry:** To complete the table: - Use the sine function on a calculator or mathematical software to find the sine values for the given angles. - For example: - Sin(0°) = 0 - Sin(30°) = 0.5 - Sin(45°) = √2/2 ≈ 0.707 - Continue this process for all listed angles. **Interactive Component:** - An input box labeled "Submit" is provided below the table for entering and submitting the calculated sine values. **Conclusion:** Understanding the sine function and its values for different angles is crucial for further studies in trigonometry and its applications. Once you've filled in the table, you'll have a clearer picture of how the sine function behaves. **Note:** Errors in sine value calculation can lead to misunderstandings in subsequent applications, so double-check your values for accuracy.
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