Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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See attached image.
Studying for exam and caught up on these two.
Thanks
![5) **Task: Graph Plotting**
Plot the following equation on the given graph. Extend the graph all the way left and right.
\[ y = 3 \cdot \sin (4\pi t - \pi) \]
**Graph Characteristics:**
- **Axes:** The horizontal axis is labeled as \( t \) and ranges from -0.25 to 1. The vertical axis is labeled as \( y \) and ranges from -4 to 4.
- **Grid:** The graph is sectioned with dotted lines to help plot the sine wave.
6) **Task: Equation Identification**
Find the equation for the graph shown below using a sine function.
**Graph Description:**
- A sine wave is plotted with two complete cycles within the interval from 0 to 0.25 on the horizontal axis.
- **Amplitude:** The wave peaks at 12 and troughs at -12, giving an amplitude of 12.
- **Periodicity:** The wave completes two full cycles in the span of 0.25 units along the x-axis.
- **Axis Lines:** Both axes are marked with units to guide the identification of critical points in the wave.
The aim is to determine the general sine equation that fits the plotted curve.](https://content.bartleby.com/qna-images/question/88ce7fe7-6055-4d88-a2fe-fb962619b6d1/37aa4bb6-b22d-4c83-a00c-dfb6a54b9c80/diht42_processed.png)
Transcribed Image Text:5) **Task: Graph Plotting**
Plot the following equation on the given graph. Extend the graph all the way left and right.
\[ y = 3 \cdot \sin (4\pi t - \pi) \]
**Graph Characteristics:**
- **Axes:** The horizontal axis is labeled as \( t \) and ranges from -0.25 to 1. The vertical axis is labeled as \( y \) and ranges from -4 to 4.
- **Grid:** The graph is sectioned with dotted lines to help plot the sine wave.
6) **Task: Equation Identification**
Find the equation for the graph shown below using a sine function.
**Graph Description:**
- A sine wave is plotted with two complete cycles within the interval from 0 to 0.25 on the horizontal axis.
- **Amplitude:** The wave peaks at 12 and troughs at -12, giving an amplitude of 12.
- **Periodicity:** The wave completes two full cycles in the span of 0.25 units along the x-axis.
- **Axis Lines:** Both axes are marked with units to guide the identification of critical points in the wave.
The aim is to determine the general sine equation that fits the plotted curve.
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(5) The graph of is as follows:
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