To determine an equation of the cosine function that has a specific period, we can use the formula for the period of a cosine function, which is given by:
\[ \text{Period} = \frac{2\pi}{|B|} \]
where \(B\) is the coefficient of \(x\) inside the cosine function.
We want the period to be \(\frac{\pi}{5}\). Setting up the equation:
\[ \frac{2\pi}{|B|} = \frac{\pi}{5} \]
We can solve for \(|B|\):
\[ |B| = 2\pi \cdot \frac{5}{\pi} = 10 \]
Thus, \(B\) must be equal to 10 (or -10, but the cosine function is even, and we typically use the positive value).
This means the function that has the desired period is:
\[ f(x) = \cos(10x) \]
Therefore, the correct answer is:
f(x) = cos(10x).
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