The period of `| cos x|`, is

Options

A. `(pi)/(2)`
B. `2pi`
C. `pi`
D. none of these

Explanation

To find the period of the function \( | \cos x | \), we can follow these steps:

### Step 1: Understand the function \( \cos x \)
The cosine function, \( \cos x \), is a periodic function with a period of \( 2\pi \). This means that \( \cos(x + 2\pi) = \cos x \) for all values of \( x \).

### Step 2: Analyze the modulus function
The modulus function \( | \cos x | \) takes all the negative values of \( \cos x \) and reflects them above the x-axis. Therefore, wherever \( \cos x \) is negative, \( | \cos x | \) will be positive.

### Step 3: Graph the function
When we graph \( \cos x \), we see that it oscillates between -1 and 1. The graph of \( | \cos x | \) will look like the graph of \( \cos x \) but with all negative parts flipped to be positive.

### Step 4: Identify the new period
The original period of \( \cos x \) is \( 2\pi \). However, since \( | \cos x | \) reflects the negative parts, we need to determine how often the pattern of \( | \cos x | \) repeats.

- From \( 0 \) to \( \pi \), \( \cos x \) goes from 1 to -1, and \( | \cos x | \) goes from 1 to 0 and then back to 1.
- From \( \pi \) to \( 2\pi \), \( \cos x \) goes from -1 back to 1, and \( | \cos x | \) goes from 0 back to 1.

Thus, the pattern of \( | \cos x | \) repeats every \( \pi \).

### Conclusion
The period of \( | \cos x | \) is \( \pi \).

### Final Answer
The period of \( | \cos x | \) is \( \pi \).

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