5. Find an equation for the graph: 1- A) y = 2 cos(3Tx) B) y = 3 cos s(x) C) y = 3 cos(2nx) D) y = 2 cos
5. Find an equation for the graph: 1- A) y = 2 cos(3Tx) B) y = 3 cos s(x) C) y = 3 cos(2nx) D) y = 2 cos
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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![**Problem 5: Find an Equation for the Graph**
The task is to determine the correct equation represented by the given graph.
### Details of the Graph:
- The graph displays a trigonometric function, specifically a cosine function, as evidenced by its wave-like pattern.
- The graph oscillates between \( y = 2 \) and \( y = -2 \), indicating that the amplitude of the function is 2.
- The graph completes a full cycle over an interval of 2 on the x-axis. This means the period of the function is 2.
### Potential Equations:
A) \( y = 2 \cos(3\pi x) \)
B) \( y = 3 \cos\left(\frac{\pi}{2} x\right) \)
C) \( y = 3 \cos(2\pi x) \)
D) \( y = 2 \cos\left(\frac{\pi}{3} x\right) \)
### Analysis:
To match the graph to one of the equations, we compare their characteristics:
1. **Amplitude:**
- The amplitude of the graph is 2.
- Therefore, the equations must have an amplitude of 2.
This eliminates options B and C, as their amplitudes are 3.
2. **Period:**
- For a cosine function \( y = A \cos(Bx) \), the period \( P \) is found using \( P = \frac{2\pi}{B} \).
- The graph's period is 2.
Let's compute the period for the remaining equations:
- For \( y = 2 \cos(3\pi x) \):
\[
P = \frac{2\pi}{3\pi} = \frac{2}{3}
\]
- For \( y = 2 \cos\left(\frac{\pi}{3} x\right) \):
\[
P = \frac{2\pi}{\frac{\pi}{3}} = 6
\]
Neither option has the correct period of 2.
#### Correct Equation:
Considering these analyses, it appears there is an error in the period calculations. Since none of the options directly provide a period of 2 with an amplitude of 2, none of the given equations perfectly matches the graph. However, in a close approximation, the period](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F357de21d-4dd5-43e5-ad45-c8ac77f9a858%2F062765f2-96ed-46ef-8d98-d430a20d18d1%2Fe12ykff.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 5: Find an Equation for the Graph**
The task is to determine the correct equation represented by the given graph.
### Details of the Graph:
- The graph displays a trigonometric function, specifically a cosine function, as evidenced by its wave-like pattern.
- The graph oscillates between \( y = 2 \) and \( y = -2 \), indicating that the amplitude of the function is 2.
- The graph completes a full cycle over an interval of 2 on the x-axis. This means the period of the function is 2.
### Potential Equations:
A) \( y = 2 \cos(3\pi x) \)
B) \( y = 3 \cos\left(\frac{\pi}{2} x\right) \)
C) \( y = 3 \cos(2\pi x) \)
D) \( y = 2 \cos\left(\frac{\pi}{3} x\right) \)
### Analysis:
To match the graph to one of the equations, we compare their characteristics:
1. **Amplitude:**
- The amplitude of the graph is 2.
- Therefore, the equations must have an amplitude of 2.
This eliminates options B and C, as their amplitudes are 3.
2. **Period:**
- For a cosine function \( y = A \cos(Bx) \), the period \( P \) is found using \( P = \frac{2\pi}{B} \).
- The graph's period is 2.
Let's compute the period for the remaining equations:
- For \( y = 2 \cos(3\pi x) \):
\[
P = \frac{2\pi}{3\pi} = \frac{2}{3}
\]
- For \( y = 2 \cos\left(\frac{\pi}{3} x\right) \):
\[
P = \frac{2\pi}{\frac{\pi}{3}} = 6
\]
Neither option has the correct period of 2.
#### Correct Equation:
Considering these analyses, it appears there is an error in the period calculations. Since none of the options directly provide a period of 2 with an amplitude of 2, none of the given equations perfectly matches the graph. However, in a close approximation, the period
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