Math Problem Statement
For a cosine function with amplitude A=0.75 and period T=10 , what is y(4) ?
Solution
We are given a cosine function with amplitude and period . To find , we can use the general form of the cosine function:
where:
- is the amplitude,
- is the period,
- is the time (or input variable),
- is the phase shift (which we assume is 0 unless specified otherwise).
Step 1: Determine the parameters
- The amplitude ,
- The period .
Substitute these into the cosine function formula:
Simplifying further:
Step 2: Find
Now, substitute into the equation:
Using a calculator to find the value of :
Thus:
Final Answer:
Would you like any further details or clarifications on this process? Here are some related questions that might interest you:
- How do you calculate the phase shift in a cosine function?
- What happens to the graph of a cosine function if the amplitude is negative?
- How do changes in the period affect the graph of a trigonometric function?
- Can you solve for the maximum and minimum values of the function for any given time?
- How would you adjust the function if the phase shift was nonzero?
Tip: When working with periodic functions like sine and cosine, it's helpful to understand how transformations such as amplitude, period, and phase shift affect the graph visually.
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Math Problem Analysis
Mathematical Concepts
Trigonometric Functions
Cosine Function
Amplitude
Period
Formulas
y(t) = A * cos((2π/T) * (t - φ))
Cosine value evaluation
Theorems
Properties of Cosine Function
Suitable Grade Level
Grades 9-12
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