Consider the following graph on the interval -210° < x < 180°: -180 -150-120 -90 -60 -30 6 4 -3 N. 2 1 1. What is the amplitude of the function? 3 2. What is the period of the function? 3. What is the equation if the function? y = 30 60 90 X 120 150
Consider the following graph on the interval -210° < x < 180°: -180 -150-120 -90 -60 -30 6 4 -3 N. 2 1 1. What is the amplitude of the function? 3 2. What is the period of the function? 3. What is the equation if the function? y = 30 60 90 X 120 150
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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The graph represents a sinusoidal function. The horizontal axis is labeled in degrees, ranging from \(-210^\circ\) to \(180^\circ\), while the vertical axis ranges from 0 to 6. The graph of the function shows one complete wave cycle starting below the horizontal axis at -180 degrees, peaking at 5 on the vertical axis, and returning downward toward the horizontal axis as it progresses toward 180 degrees.
**Detailed Steps to Interpret the Graph:**
1. **Amplitude:** The amplitude is the maximum distance from the average value (or equilibrium position) of the wave. In this case, the wave oscillates from 0 to 5, giving an amplitude of 5.
2. **Period:** The period is the horizontal length it takes for the function to complete one full cycle. By examining the graph, the wave completes one full cycle from -180 degrees to 150 degrees, implying a period approximately equal to 360 degrees.
3. **Equation:** The general form of a sinusoidal function is \(y = A \sin(Bx + C) + D\), where:
- \(A\) is the amplitude,
- \(B\) affects the period,
- \(C\) is the horizontal shift,
- \(D\) is the vertical shift.
Use the information from the graph to derive these values.
### Questions:
1. **What is the amplitude of the function?**
- Answer: \(5\) (The correct answer should be provided instead of the incorrectly marked \(3\).)
2. **What is the period of the function?**
- Answer: Provide the value (In the context, the period can be derived as \(360\) degrees.)
3. **What is the equation of the function?**
- Answer: Derive and provide the equation based on observed amplitude, period, and any phase shift or vertical translations.
### Learning Points:
- Identifying the characteristics of sinusoidal functions.
- Understanding the graph of sine or cosine functions.
- Calculating amplitude, period, and writing the function's equation.
*[Insert any additional background knowledge on sinusoidal functions or related exercises here for further learning.]*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3f56dff-0b60-49cc-8c03-28401888e8a6%2F55ef1e65-c8aa-4b08-877a-939df9c2de64%2Fdaft7j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Consider the following graph on the interval \(-210^\circ < x < 180^\circ\):
The graph represents a sinusoidal function. The horizontal axis is labeled in degrees, ranging from \(-210^\circ\) to \(180^\circ\), while the vertical axis ranges from 0 to 6. The graph of the function shows one complete wave cycle starting below the horizontal axis at -180 degrees, peaking at 5 on the vertical axis, and returning downward toward the horizontal axis as it progresses toward 180 degrees.
**Detailed Steps to Interpret the Graph:**
1. **Amplitude:** The amplitude is the maximum distance from the average value (or equilibrium position) of the wave. In this case, the wave oscillates from 0 to 5, giving an amplitude of 5.
2. **Period:** The period is the horizontal length it takes for the function to complete one full cycle. By examining the graph, the wave completes one full cycle from -180 degrees to 150 degrees, implying a period approximately equal to 360 degrees.
3. **Equation:** The general form of a sinusoidal function is \(y = A \sin(Bx + C) + D\), where:
- \(A\) is the amplitude,
- \(B\) affects the period,
- \(C\) is the horizontal shift,
- \(D\) is the vertical shift.
Use the information from the graph to derive these values.
### Questions:
1. **What is the amplitude of the function?**
- Answer: \(5\) (The correct answer should be provided instead of the incorrectly marked \(3\).)
2. **What is the period of the function?**
- Answer: Provide the value (In the context, the period can be derived as \(360\) degrees.)
3. **What is the equation of the function?**
- Answer: Derive and provide the equation based on observed amplitude, period, and any phase shift or vertical translations.
### Learning Points:
- Identifying the characteristics of sinusoidal functions.
- Understanding the graph of sine or cosine functions.
- Calculating amplitude, period, and writing the function's equation.
*[Insert any additional background knowledge on sinusoidal functions or related exercises here for further learning.]*
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