Math Problem Statement
the highest is 5 & lowest is 1
Solution
Thank you for the correction. Let's update the calculations based on the highest value being 5 and the lowest value being 1.
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Amplitude:
- The amplitude is the distance from the midline of the graph to the peak or trough.
- From the graph, the highest point is 5 and the lowest point is 1.
- The amplitude is given by .
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Period:
- The period is the distance over which the function repeats itself.
- We see that one full cycle occurs between and .
- Thus, the period is 100 units.
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Phase Shift:
- For a cosine function, a phase shift occurs if the graph is shifted horizontally.
- Here, the graph appears to start at its maximum value at , indicating there is no horizontal shift.
- Therefore, the phase shift is 0.
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Axis of Curve:
- The axis of the curve (or the midline) is the horizontal line around which the graph oscillates.
- The midline can be found by taking the average of the maximum and minimum values.
- The midline is .
Based on the updated analysis, we fill in the table as follows:
\hline \text{AMPLITUDE} & \text{PERIOD} & \text{PHASE SHIFT} & \text{AXIS OF CURVE} \\ \hline 2 & 100 & 0 & y = 3 \\ \hline \end{array}$$ Would you like more details on any of these parameters or have any questions? Here are five additional questions you might consider: 1. How would the graph change if the amplitude were doubled? 2. What is the effect of a non-zero phase shift on the graph? 3. How do we determine the frequency of the cosine function from the period? 4. How would the graph be affected if the midline were shifted up by 2 units? 5. Can you explain the relationship between the period and the wavelength of the cosine function? **Tip**: Always ensure the accuracy of the maximum and minimum values before calculating the amplitude and midline for more precise analysis of trigonometric functions.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Cosine Function
Formulas
Amplitude calculation
Theorems
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Suitable Grade Level
High School
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