Find a function of the form y = A sin(ka)+ C or y = A cos(kr) + C whose graph matches this one: %3D 16-15-14-13-N 10 o Leave your answer in exact form; if necessary, type pi for T.
Find a function of the form y = A sin(ka)+ C or y = A cos(kr) + C whose graph matches this one: %3D 16-15-14-13-N 10 o Leave your answer in exact form; if necessary, type pi for T.
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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Question
![## Problem Statement
**Find a function of the form**
\[ y = A \sin(kx) + C \quad \text{or} \quad y = A \cos(kx) + C \]
**whose graph matches this one:**
### Graph Explanation
- **Axes:** The graph is plotted on a Cartesian plane with x-axis and y-axis.
- **X-axis Range:** The x-values range from approximately \(-12\) to \(12\).
- **Y-axis Range:** The y-values range from \(-6\) to \(6\).
- **Graph Description:** The graph is a sinusoidal wave, starting at a negative value, peaking in the negative direction, and forming a wave pattern that crosses the x-axis.
### Key Characteristics of the Wave:
- **Amplitude (A):** The maximum value (height) of the wave from the centerline (axis).
- **Period (P):** The length of one complete cycle of the wave. This is the distance between repeating points, measured along the x-axis.
- **Vertical Shift (C):** The upward or downward displacement of the wave from the standard position (\(y = 0\)).
**Leave your answer in exact form; if necessary, type `pi` for \(\pi\).**
**Answer Box:**
\[ y = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fc3766d-bc8c-44dc-b95b-e319f0e06bc0%2Fd6344c2a-fff0-44b9-b2ba-38e9346cd621%2Flp7wses_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem Statement
**Find a function of the form**
\[ y = A \sin(kx) + C \quad \text{or} \quad y = A \cos(kx) + C \]
**whose graph matches this one:**
### Graph Explanation
- **Axes:** The graph is plotted on a Cartesian plane with x-axis and y-axis.
- **X-axis Range:** The x-values range from approximately \(-12\) to \(12\).
- **Y-axis Range:** The y-values range from \(-6\) to \(6\).
- **Graph Description:** The graph is a sinusoidal wave, starting at a negative value, peaking in the negative direction, and forming a wave pattern that crosses the x-axis.
### Key Characteristics of the Wave:
- **Amplitude (A):** The maximum value (height) of the wave from the centerline (axis).
- **Period (P):** The length of one complete cycle of the wave. This is the distance between repeating points, measured along the x-axis.
- **Vertical Shift (C):** The upward or downward displacement of the wave from the standard position (\(y = 0\)).
**Leave your answer in exact form; if necessary, type `pi` for \(\pi\).**
**Answer Box:**
\[ y = \]
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