Math Problem Statement
Solution
To determine the period of the sinusoidal function, we analyze the given data:
Key points from the problem:
- The function has maximums at and .
- The function has a minimum at .
- The -axis is in radians, and the function is sinusoidal.
Step-by-step solution:
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Distance between two maximums:
The distance between consecutive maximum points on a sinusoidal graph is half the period of the function.The -coordinates of the maximum points are and .
The distance between these points is:Hence, the distance between consecutive maximums is , which equals half the period.
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Calculate the period:
Since the distance between consecutive maximums is , where is the period, we find:
Final Answer:
The period of the sinusoidal function is:
Would you like a more detailed explanation or visual representation of the solution?
Here are 5 related questions for practice:
- How would the period change if the function were horizontally stretched instead of compressed?
- What is the amplitude of the function given the maximum and minimum values?
- How would you determine the phase shift of this sinusoidal function?
- How do you write the equation of the function in terms of sine or cosine?
- What is the frequency of the function in terms of ?
Tip: When dealing with sinusoidal functions, always consider how the period is related to the distance between peaks or troughs!
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Math Problem Analysis
Mathematical Concepts
Sinusoidal Functions
Trigonometry
Periodicity
Formulas
Period = 2 * (distance between consecutive maximums)
Theorems
Periodicity of Sinusoidal Functions
Suitable Grade Level
Grades 9-11