8 The image depicts a graph of the trigonometric function $ y = \sin(x) $ with specific modifications. ### Description of the Graph:- **Axes:** The graph features the horizontal $ x $-axis and the vertical $ y $-axis.- **Function:** The blue curve represents a sine wave, a periodic function, which oscillates above and below the $ x $-axis. ### Details of the Sine Wave:- **Amplitude:** The maximum height and depth of the wave from the center line (y = 0) are approximately 4 units. This suggests a vertical scaling factor has been applied. - **Period:** The wave cycles with a period of $ 6\pi $, indicating a horizontal stretching was applied. - **X-Axis Intervals:** - Marked intervals include $-\frac{3\pi}{2}$, $-\frac{3\pi}{4}$, $ \frac{3\pi}{4}$, $\frac{3\pi}{2}$, $\frac{9\pi}{4}$, $\frac{3\pi}{2}$, $\frac{15\pi}{4}$, and $\frac{9\pi}{2}$. - **Y-Axis Intervals:** - The scale on the $ y $-axis extends from -4 to 4, with notable points at each integer. ### Key Observations:- The sine wave completes one full cycle from $-\frac{3\pi}{2}$ to $\frac{9\pi}{2}$.- Peaks occur at approximately $(\frac{3\pi}{4}, 4)$ and $(\frac{15\pi}{4}, 4)$.- Troughs occur at approximately positions $(\frac{9\pi}{4}, -4)$.- The points of intersection with the $ x $-axis occur at multiples of $\frac{3\pi}{2}$.This graph is suitable for education on transformations of sine waves, illustrating vertical scaling and horizontal stretching/compression effectively. **Instructions:**Write an equation of the form $ y = a \sin bx $ or $ y = a \cos bx $ to describe the graph below.**Graph Explanation:**The graph depicts a sinusoidal wave typically associated with either a sine or cosine function. To determine whether to use sine or cosine, one should examine the starting point of the wave. If the wave starts at the midline and moves upwards, it resembles a sine function. If it starts at a maximum or minimum, it is likely a cosine function.Key characteristics to analyze include:- **Amplitude ($a$)**: This is the distance from the midline to the peak of the wave.- **Period**: The length of one complete cycle of the wave. The value $b$ in the equations $ y = a \sin bx $ or $ y = a \cos bx $ affects the period, calculated as $ \frac{2\pi}{b} $.- **Phase Shift**: Any horizontal shift from the origin, which would modify the basic sine or cosine function.- **Vertical Shift**: Any upward or downward translations from the midline.Use these parameters to write the equation that accurately describes the specific characteristics of the graph shown.

Name: 8 The image depicts a graph of the trigonometric function $ y = \sin(
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Description: 8 The image depicts a graph of the trigonometric function \( y = \sin(x) $ with specific modifications. ### Description of the Graph:- **Axes:** The graph features the horizontal $ x $-axis and the vertical $ y $-axis.- **Function:** The blue cu

Answered: y 4- 3구 9n 151 9 - 4 4 2 4 4 -3- -4

Math

Advanced Math

y 4- 3구 9n 151 9 - 4 4 2 4 4 -3- -4

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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Topic Video

Question

The image depicts a graph of the trigonometric function $ y = \sin(x) $ with specific modifications.

### Description of the Graph:

- **Axes:** The graph features the horizontal $ x $-axis and the vertical $ y $-axis.
- **Function:** The blue curve represents a sine wave, a periodic function, which oscillates above and below the $ x $-axis.

### Details of the Sine Wave:

- **Amplitude:** The maximum height and depth of the wave from the center line (y = 0) are approximately 4 units. This suggests a vertical scaling factor has been applied.

- **Period:** The wave cycles with a period of $ 6\pi $, indicating a horizontal stretching was applied.

- **X-Axis Intervals:**
- Marked intervals include $-\frac{3\pi}{2}$, $-\frac{3\pi}{4}$, $ \frac{3\pi}{4}$, $\frac{3\pi}{2}$, $\frac{9\pi}{4}$, $\frac{3\pi}{2}$, $\frac{15\pi}{4}$, and $\frac{9\pi}{2}$.

- **Y-Axis Intervals:**
- The scale on the $ y $-axis extends from -4 to 4, with notable points at each integer.

### Key Observations:

- The sine wave completes one full cycle from $-\frac{3\pi}{2}$ to $\frac{9\pi}{2}$.
- Peaks occur at approximately $(\frac{3\pi}{4}, 4)$ and $(\frac{15\pi}{4}, 4)$.
- Troughs occur at approximately positions $(\frac{9\pi}{4}, -4)$.
- The points of intersection with the $ x $-axis occur at multiples of $\frac{3\pi}{2}$.

This graph is suitable for education on transformations of sine waves, illustrating vertical scaling and horizontal stretching/compression effectively.

**Instructions:**

Write an equation of the form $ y = a \sin bx $ or $ y = a \cos bx $ to describe the graph below.

**Graph Explanation:**

The graph depicts a sinusoidal wave typically associated with either a sine or cosine function. To determine whether to use sine or cosine, one should examine the starting point of the wave. If the wave starts at the midline and moves upwards, it resembles a sine function. If it starts at a maximum or minimum, it is likely a cosine function.

Key characteristics to analyze include:

- **Amplitude ($a$)**: This is the distance from the midline to the peak of the wave.
- **Period**: The length of one complete cycle of the wave. The value $b$ in the equations $ y = a \sin bx $ or $ y = a \cos bx $ affects the period, calculated as $ \frac{2\pi}{b} $.
- **Phase Shift**: Any horizontal shift from the origin, which would modify the basic sine or cosine function.
- **Vertical Shift**: Any upward or downward translations from the midline.

Use these parameters to write the equation that accurately describes the specific characteristics of the graph shown.

Expert Solution

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The function is y=4sin(2x/3)

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