7. Consider the trigonometric graph shown below. The coordinates of the horizontal intercepts are (좋). (품). and (F.0) 1.0T y 0.8- 0.6- 0.2- -10 -8 -2 10 X -0.2+ -0.4- -0.6 -0.8 - -1.0- Except for the amplitude, the rest of the answers should be in terms of r and not decimals a. Find the period and the amplitude of the graph shown b. Find an equation for the graph using a sine function. c. Find an equation for the graph using a cosine function.
7. Consider the trigonometric graph shown below. The coordinates of the horizontal intercepts are (좋). (품). and (F.0) 1.0T y 0.8- 0.6- 0.2- -10 -8 -2 10 X -0.2+ -0.4- -0.6 -0.8 - -1.0- Except for the amplitude, the rest of the answers should be in terms of r and not decimals a. Find the period and the amplitude of the graph shown b. Find an equation for the graph using a sine function. c. Find an equation for the graph using a cosine function.
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![### Trigonometric Graph Analysis
Consider the trigonometric graph shown below. The coordinates of the horizontal intercepts are:
\[ \left(-\frac{7\pi}{4}, 0\right), \quad \left(\frac{\pi}{4}, 0\right), \quad \text{and} \quad \left(\frac{9\pi}{4}, 0\right) \]
#### Graph Description
Within the graph, the x-axis is labeled from -10 to 10, and the y-axis is labeled from -1.0 to 1.0, depicting the typical range of a trigonometric function such as sine or cosine. The function intercepts the x-axis at specific points denoted in terms of \(\pi\) as mentioned above.
The graph itself shows one complete cycle of a wave starting at \(\left(-\frac{7\pi}{4}, 0\right)\) and ending at \(\left(\frac{9\pi}{4}, 0\right)\).
Below the graph are three questions:
### Tasks
**Except for the amplitude, the rest of the answers should be in terms of \(\pi\) and not decimals**
1. **Find the period and the amplitude of the graph shown.**
2. **Find an equation for the graph using a sine function.**
3. **Find an equation for the graph using a cosine function.**
#### Part (a)
- **Period**: The period of the function is the length of one complete cycle. Observe the x-coordinates of the intercepts \(\left(-\frac{7\pi}{4}, 0\right)\) and \(\left(\frac{9\pi}{4}, 0\right)\) to find the period.
- **Amplitude**: The amplitude is the maximum absolute value of the y-coordinates.
#### Part (b)
- **Sine Function**: Use the form \(y = A \sin(Bx - C) + D\) to find the sine function that matches the graph.
#### Part (c)
- **Cosine Function**: Use the form \(y = A \cos(Bx - C) + D\) to find the cosine function that matches the graph.
This lesson aims to explore how to determine the features and equations of trigonometric functions based on their graphical representations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff62d5ca7-5439-4cfe-bb83-29d1381eaedb%2F392e4c22-d8de-4311-974a-e3bc0e893f36%2F3q20qwe_processed.png&w=3840&q=75)
Transcribed Image Text:### Trigonometric Graph Analysis
Consider the trigonometric graph shown below. The coordinates of the horizontal intercepts are:
\[ \left(-\frac{7\pi}{4}, 0\right), \quad \left(\frac{\pi}{4}, 0\right), \quad \text{and} \quad \left(\frac{9\pi}{4}, 0\right) \]
#### Graph Description
Within the graph, the x-axis is labeled from -10 to 10, and the y-axis is labeled from -1.0 to 1.0, depicting the typical range of a trigonometric function such as sine or cosine. The function intercepts the x-axis at specific points denoted in terms of \(\pi\) as mentioned above.
The graph itself shows one complete cycle of a wave starting at \(\left(-\frac{7\pi}{4}, 0\right)\) and ending at \(\left(\frac{9\pi}{4}, 0\right)\).
Below the graph are three questions:
### Tasks
**Except for the amplitude, the rest of the answers should be in terms of \(\pi\) and not decimals**
1. **Find the period and the amplitude of the graph shown.**
2. **Find an equation for the graph using a sine function.**
3. **Find an equation for the graph using a cosine function.**
#### Part (a)
- **Period**: The period of the function is the length of one complete cycle. Observe the x-coordinates of the intercepts \(\left(-\frac{7\pi}{4}, 0\right)\) and \(\left(\frac{9\pi}{4}, 0\right)\) to find the period.
- **Amplitude**: The amplitude is the maximum absolute value of the y-coordinates.
#### Part (b)
- **Sine Function**: Use the form \(y = A \sin(Bx - C) + D\) to find the sine function that matches the graph.
#### Part (c)
- **Cosine Function**: Use the form \(y = A \cos(Bx - C) + D\) to find the cosine function that matches the graph.
This lesson aims to explore how to determine the features and equations of trigonometric functions based on their graphical representations.
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