amplitude and periode
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Understanding Amplitude and Period of a Sine Function
#### Problem Statement:
Determine the amplitude and period of the following function. Then, graph the function.
\[ y = 8 \sin x \]
#### Key Components to Solve:
1. **Amplitude**:
- The amplitude is the absolute value of the coefficient of the sine function.
- In this function, the amplitude is \(|8|\), which equals **8**.
2. **Period**:
- The period of a sine function \(\sin(bx)\) is given by the formula \(\frac{2\pi}{|b|}\).
- Here, \(b = 1\). Thus, the period is \(\frac{2\pi}{1} = 2\pi\).
3. **Graphing the Function**:
- Use the graphing tool to visualize the sine wave with an amplitude of 8 and a period of \(2\pi\).
#### Graph Explanation:
- A graph is provided on the right side with a grid ranging from -10 to 10 on both axes.
- The graph includes a sine wave, showing its periodic nature.
- The wave peaks at 8 and troughs at -8, consistent with an amplitude of 8.
- The wave completes one full cycle every \(2\pi\) units along the x-axis.
#### Instructions:
- Use the graphing tool to input and adjust your function as needed.
- Ensure the graph accurately reflects the function's amplitude and period.
#### Note:
- For any calculations, use exact answers with the symbol \(\pi\) when necessary.
- Click "Save for Later" to store your progress.
Feel free to use this guide to help you understand and visualize the properties of sine functions!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dd0ebbe-8030-4b7a-b11b-0fd9a7ecabfc%2F833d7e09-2567-4a97-9496-6745b83cccc1%2F73x7glp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Amplitude and Period of a Sine Function
#### Problem Statement:
Determine the amplitude and period of the following function. Then, graph the function.
\[ y = 8 \sin x \]
#### Key Components to Solve:
1. **Amplitude**:
- The amplitude is the absolute value of the coefficient of the sine function.
- In this function, the amplitude is \(|8|\), which equals **8**.
2. **Period**:
- The period of a sine function \(\sin(bx)\) is given by the formula \(\frac{2\pi}{|b|}\).
- Here, \(b = 1\). Thus, the period is \(\frac{2\pi}{1} = 2\pi\).
3. **Graphing the Function**:
- Use the graphing tool to visualize the sine wave with an amplitude of 8 and a period of \(2\pi\).
#### Graph Explanation:
- A graph is provided on the right side with a grid ranging from -10 to 10 on both axes.
- The graph includes a sine wave, showing its periodic nature.
- The wave peaks at 8 and troughs at -8, consistent with an amplitude of 8.
- The wave completes one full cycle every \(2\pi\) units along the x-axis.
#### Instructions:
- Use the graphing tool to input and adjust your function as needed.
- Ensure the graph accurately reflects the function's amplitude and period.
#### Note:
- For any calculations, use exact answers with the symbol \(\pi\) when necessary.
- Click "Save for Later" to store your progress.
Feel free to use this guide to help you understand and visualize the properties of sine functions!
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