### Problem Description#### Objective:Determine the amplitude, period, and phase shift of the given cosine graph. Then, use that information to write an equation of the graph in the form $ y = a \cos(bx - c) $. Use a positive amplitude in the equation.**Graph Description:**The provided graph shows a wave-like pattern typical of a cosine function. Key points are highlighted along the x-axis at intervals of $\frac{\pi}{4}$.#### Tasks:1. **Amplitude:** Determine the amplitude of the cosine graph.2. **Period:** Determine the period of the cosine graph.3. **Phase Shift:** Determine the phase shift of the cosine graph.4. **Equation:** Write the equation using the determined amplitude, period, and phase shift.| Amplitude: | ________ || ----------- | --- || Period: | ________ || Phase Shift: | ________ || Equation: | _____________________ |#### Next Steps:2. **Redo the problem:** Write it as a sine function in the form $ y = a \sin(bx - c) $, where $ a $ > 0 and the phase shift is between 0 and $ 2\pi $. Use a positive amplitude $ a $ in the equation.| Amplitude: | ________ || ----------- | --- || Period: | ________ || Phase Shift: | ________ || Equation: | _____________________ |#### Explanation of the Diagram:- The x-axis is marked in terms of $\pi$ with key points at intervals such as $ \frac{\pi}{4} $, $ \frac{\pi}{2} $, and so on up to $ 2\pi $.- The y-axis shows the positive and negative peaks of the graph, which are labeled as amplitude $ A $ and $-A $ respectively.- The waveform oscillates in a manner typical of a cosine function, indicating the characteristic peaks and troughs.By analyzing the graph and completing the table, you will utilize these measurements to formulate the respective cosine and sine equations as described.

By using trigonometric properties

Tlumbers, When aPplicabie. 1. Determine the amplitude, period, and phase shift of the cosine graph. Then use that informat write an equation of the graph of the form y =acos(bx-c). Use a positive amplitude a in the ec -1 Amplitude: ; Period: ; Phase Shift: Equation: 2. Now redo problem 1, but write it as a sine function of the form y=asin(bx- c) where a > 0 and the phase shift is between 0 and 27. Use a positive amplitude a in the equati Phase Shift: Equation:

Tlumbers, When aPplicabie. 1. Determine the amplitude, period, and phase shift of the cosine graph. Then use that informat write an equation of the graph of the form y =acos(bx-c). Use a positive amplitude a in the ec -1 Amplitude: ; Period: ; Phase Shift: Equation: 2. Now redo problem 1, but write it as a sine function of the form y=asin(bx- c) where a > 0 and the phase shift is between 0 and 27. Use a positive amplitude a in the equati Phase Shift: Equation:

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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### Problem Description

#### Objective:
Determine the amplitude, period, and phase shift of the given cosine graph. Then, use that information to write an equation of the graph in the form $ y = a \cos(bx - c) $. Use a positive amplitude in the equation.

**Graph Description:**
The provided graph shows a wave-like pattern typical of a cosine function. Key points are highlighted along the x-axis at intervals of $\frac{\pi}{4}$.

#### Tasks:
1. **Amplitude:** Determine the amplitude of the cosine graph.
2. **Period:** Determine the period of the cosine graph.
3. **Phase Shift:** Determine the phase shift of the cosine graph.
4. **Equation:** Write the equation using the determined amplitude, period, and phase shift.

| Amplitude: | ________ |
| ----------- | --- |
| Period: | ________ |
| Phase Shift: | ________ |
| Equation: | _____________________ |

#### Next Steps:
2. **Redo the problem:** Write it as a sine function in the form $ y = a \sin(bx - c) $, where $ a $ > 0 and the phase shift is between 0 and $ 2\pi $. Use a positive amplitude $ a $ in the equation.

| Amplitude: | ________ |
| ----------- | --- |
| Period: | ________ |
| Phase Shift: | ________ |
| Equation: | _____________________ |

#### Explanation of the Diagram:
- The x-axis is marked in terms of $\pi$ with key points at intervals such as $ \frac{\pi}{4} $, $ \frac{\pi}{2} $, and so on up to $ 2\pi $.
- The y-axis shows the positive and negative peaks of the graph, which are labeled as amplitude $ A $ and $-A $ respectively.
- The waveform oscillates in a manner typical of a cosine function, indicating the characteristic peaks and troughs.

By analyzing the graph and completing the table, you will utilize these measurements to formulate the respective cosine and sine equations as described.

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