Use the graph shown below to answer the questions. y 10 5 X 4 8 (a) Amplitude = (b) Period = X (C) Write an equation for the graph. Use y as the dependent variable and x as the independent variable. Note: Using sine instead of cosine is probably better here.
Use the graph shown below to answer the questions. y 10 5 X 4 8 (a) Amplitude = (b) Period = X (C) Write an equation for the graph. Use y as the dependent variable and x as the independent variable. Note: Using sine instead of cosine is probably better here.
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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Use graph to find the amplitude, period and write an equation using sine.
![### Wave Function Analysis
#### Graph Description
The graph presented is a sine wave plotted on a coordinate plane where the horizontal axis (x-axis) represents the independent variable \( x \), and the vertical axis (y-axis) represents the dependent variable \( y \). The wave starts at \( x = 0 \) with a value of \( y = 5 \), reaches its maximum at \( x \approx 2 \) with \( y = 10 \), its minimum at \( x \approx 6 \) with \( y \approx 0 \), and appears to complete one period at \( x \approx 8 \).
#### Questions
1. **(a) Amplitude:**
- The amplitude of a wave, which is the peak value, can be calculated as half the vertical distance between the maximum and minimum values of the wave. Therefore:
\[
\text{Amplitude} = \frac{\text{maximum value} - \text{minimum value}}{2}
\]
Fill in your answer here: \_\_\_\_\_
2. **(b) Period:**
- The period of a wave is the horizontal distance (along the x-axis) over which the wave repeats itself. From the provided graph, estimate the distance:
\[
\text{Period} = \_\_\_\_\_
\]
(There is an indicator here suggesting that the provided answer might be incorrect.)
3. **(c) Write an Equation:**
- Write an equation for the graph, using \( y \) as the dependent variable and \( x \) as the independent variable. Note: The suggestion hints that using sine might be more suitable than cosine for describing the wave.
\[
y = \_\_\_\_\_
\]
#### Notes
- To determine the equation accurately, observe the initial phase shift and vertical shift of the wave.
- Considering the form of the sine function \( y = A \sin(Bx + C) + D \), where:
- \( A \) is the amplitude,
- \( B \) relates to the period \( \left( B = \frac{2\pi}{\text{period}} \right) \),
- \( C \) is the phase shift,
- \( D \) is the vertical shift.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedc716be-e066-4234-bd1a-1a86837575c3%2F5bbbf93b-2ee8-473b-936d-425b7e58d1a7%2Feetsqwp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Wave Function Analysis
#### Graph Description
The graph presented is a sine wave plotted on a coordinate plane where the horizontal axis (x-axis) represents the independent variable \( x \), and the vertical axis (y-axis) represents the dependent variable \( y \). The wave starts at \( x = 0 \) with a value of \( y = 5 \), reaches its maximum at \( x \approx 2 \) with \( y = 10 \), its minimum at \( x \approx 6 \) with \( y \approx 0 \), and appears to complete one period at \( x \approx 8 \).
#### Questions
1. **(a) Amplitude:**
- The amplitude of a wave, which is the peak value, can be calculated as half the vertical distance between the maximum and minimum values of the wave. Therefore:
\[
\text{Amplitude} = \frac{\text{maximum value} - \text{minimum value}}{2}
\]
Fill in your answer here: \_\_\_\_\_
2. **(b) Period:**
- The period of a wave is the horizontal distance (along the x-axis) over which the wave repeats itself. From the provided graph, estimate the distance:
\[
\text{Period} = \_\_\_\_\_
\]
(There is an indicator here suggesting that the provided answer might be incorrect.)
3. **(c) Write an Equation:**
- Write an equation for the graph, using \( y \) as the dependent variable and \( x \) as the independent variable. Note: The suggestion hints that using sine might be more suitable than cosine for describing the wave.
\[
y = \_\_\_\_\_
\]
#### Notes
- To determine the equation accurately, observe the initial phase shift and vertical shift of the wave.
- Considering the form of the sine function \( y = A \sin(Bx + C) + D \), where:
- \( A \) is the amplitude,
- \( B \) relates to the period \( \left( B = \frac{2\pi}{\text{period}} \right) \),
- \( C \) is the phase shift,
- \( D \) is the vertical shift.
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