The image displays a trigonometric function and prompts for analyzing its properties. The function given is: \[ g(x) = \cos\left(2\left(x - \frac{\pi}{4}\right)\right) \] The information to be determined includes: 1. **Amplitude**: This is the maximum value of the cosine function from its mid-line. For a standard cosine function \( a \cos(bx + c) \), the amplitude is \(|a|\). 2. **Equation of Mid-line**: This is the horizontal line that runs through the middle of the graph of the function, essentially the average value of the maximum and minimum value of the function. 3. **Length of Period**: This tells us how long it takes for the function to complete one full cycle. For a cosine function \( a \cos(bx + c) \), the period is \(\frac{2\pi}{|b|}\). 4. **Phase Shift**: This is the horizontal shift from the origin. It is calculated from the expression \(-\frac{c}{b}\) for a general function \( a \cos(bx + c) \). The image does not contain any graphs or diagrams to describe further.
The image displays a trigonometric function and prompts for analyzing its properties. The function given is: \[ g(x) = \cos\left(2\left(x - \frac{\pi}{4}\right)\right) \] The information to be determined includes: 1. **Amplitude**: This is the maximum value of the cosine function from its mid-line. For a standard cosine function \( a \cos(bx + c) \), the amplitude is \(|a|\). 2. **Equation of Mid-line**: This is the horizontal line that runs through the middle of the graph of the function, essentially the average value of the maximum and minimum value of the function. 3. **Length of Period**: This tells us how long it takes for the function to complete one full cycle. For a cosine function \( a \cos(bx + c) \), the period is \(\frac{2\pi}{|b|}\). 4. **Phase Shift**: This is the horizontal shift from the origin. It is calculated from the expression \(-\frac{c}{b}\) for a general function \( a \cos(bx + c) \). The image does not contain any graphs or diagrams to describe further.
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°.
Related questions
Question
![The image displays a trigonometric function and prompts for analyzing its properties. The function given is:
\[ g(x) = \cos\left(2\left(x - \frac{\pi}{4}\right)\right) \]
The information to be determined includes:
1. **Amplitude**: This is the maximum value of the cosine function from its mid-line. For a standard cosine function \( a \cos(bx + c) \), the amplitude is \(|a|\).
2. **Equation of Mid-line**: This is the horizontal line that runs through the middle of the graph of the function, essentially the average value of the maximum and minimum value of the function.
3. **Length of Period**: This tells us how long it takes for the function to complete one full cycle. For a cosine function \( a \cos(bx + c) \), the period is \(\frac{2\pi}{|b|}\).
4. **Phase Shift**: This is the horizontal shift from the origin. It is calculated from the expression \(-\frac{c}{b}\) for a general function \( a \cos(bx + c) \).
The image does not contain any graphs or diagrams to describe further.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F446d612d-b997-4951-bf61-55214d1953ff%2F013c9d65-fb6a-4cdf-aa6c-1a778f383c52%2Fc7cazl5.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a trigonometric function and prompts for analyzing its properties. The function given is:
\[ g(x) = \cos\left(2\left(x - \frac{\pi}{4}\right)\right) \]
The information to be determined includes:
1. **Amplitude**: This is the maximum value of the cosine function from its mid-line. For a standard cosine function \( a \cos(bx + c) \), the amplitude is \(|a|\).
2. **Equation of Mid-line**: This is the horizontal line that runs through the middle of the graph of the function, essentially the average value of the maximum and minimum value of the function.
3. **Length of Period**: This tells us how long it takes for the function to complete one full cycle. For a cosine function \( a \cos(bx + c) \), the period is \(\frac{2\pi}{|b|}\).
4. **Phase Shift**: This is the horizontal shift from the origin. It is calculated from the expression \(-\frac{c}{b}\) for a general function \( a \cos(bx + c) \).
The image does not contain any graphs or diagrams to describe further.
Expert Solution
Step 1
Given:-
g(x) = cos(2(x-π/4))
To find
- Amplitude
- Equation of midline
- length of period
- phase shift
Step by step
Solved in 5 steps
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