**Transcription of Educational Content:**Graph Analysis of Sinusoidal Function**Objective:** Provide the graph of the sinusoidal function over the interval $[0, 24]$.**Function:** \[ f(x) = 6 \cos \left( \frac{\pi}{5} (x - 3) \right) + 2 \]**Characteristics to Identify:**| Characteristic | Description ||-----------------------|-------------|| Amplitude | || Vertical Translation | || Horizontal Dilation | || Phase Shift | || Period | |**Graph Description:**The graph represents a cosine function plotted on an interval from 0 to 24. The x-axis is scaled in numeric radians with $\pi$ approximately equal to 3.14. The function demonstrates regular oscillations typical of a cosine wave. **Key Features to Analyze:**- **Amplitude:** This is the height from the middle of the wave to its peak. The graph has an amplitude of 6.- **Vertical Translation:** The graph shifts vertically by 2 units upwards.- **Horizontal Dilation:** The horizontal stretch/compression factor due to the $\frac{\pi}{5}$ in the function.- **Phase Shift:** The graph shifts horizontally by 3 units to the right.- **Period:** The period can be calculated using the formula $ \frac{2\pi}{\text{horizontal dilation factor}} $.These elements illustrate the transformations applied to the basic cosine function, resulting in the specific wave characteristics represented on the graph.

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Description: **Transcription of Educational Content:**Graph Analysis of Sinusoidal Function**Objective:** Provide the graph of the sinusoidal function over the interval $[0, 24]$.**Function:** \[ f(x) = 6 \cos \left( \frac{\pi}{5} (x - 3) \right) + 2 \]**Cha

If y = A sin(B(x + C)) + D then amplitude is A period is 2π/B phase shift is C (positive…

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Trigonometry

3. Provide the graph of the sinusoidal function over the interval [0, 24). f(x) = 6 cos + 2 %3D Identify the following characteristics of f(x) Amplitude Vertical translation Horizontal dilation Phase Shift Period

3. Provide the graph of the sinusoidal function over the interval [0, 24). f(x) = 6 cos + 2 %3D Identify the following characteristics of f(x) Amplitude Vertical translation Horizontal dilation Phase Shift Period

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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**Transcription of Educational Content:**

Graph Analysis of Sinusoidal Function

**Objective:**
Provide the graph of the sinusoidal function over the interval $[0, 24]$.

**Function:**
\[ f(x) = 6 \cos \left( \frac{\pi}{5} (x - 3) \right) + 2 \]

**Characteristics to Identify:**

| Characteristic | Description |
|-----------------------|-------------|
| Amplitude | |
| Vertical Translation | |
| Horizontal Dilation | |
| Phase Shift | |
| Period | |

**Graph Description:**

The graph represents a cosine function plotted on an interval from 0 to 24. The x-axis is scaled in numeric radians with $\pi$ approximately equal to 3.14. The function demonstrates regular oscillations typical of a cosine wave.

**Key Features to Analyze:**

- **Amplitude:** This is the height from the middle of the wave to its peak. The graph has an amplitude of 6.
- **Vertical Translation:** The graph shifts vertically by 2 units upwards.
- **Horizontal Dilation:** The horizontal stretch/compression factor due to the $\frac{\pi}{5}$ in the function.
- **Phase Shift:** The graph shifts horizontally by 3 units to the right.
- **Period:** The period can be calculated using the formula $ \frac{2\pi}{\text{horizontal dilation factor}} $.

These elements illustrate the transformations applied to the basic cosine function, resulting in the specific wave characteristics represented on the graph.

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