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
The function we are analyzing is \( | \cos x | \). The cosine function, \( \cos x \), has a period of \( 2\pi \). However, since we are taking the absolute value, we need to determine how this affects the period.

**Hint:** Recall that the period of a function is the smallest positive value \( T \) such that \( f(x + T) = f(x) \) for all \( x \).

### Step 2: Analyze the behavior of \( | \cos x | \)
The cosine function oscillates between -1 and 1. When we take the absolute value, the negative parts of the cosine wave will be reflected above the x-axis. Therefore, \( | \cos x | \) will have the same peaks as \( \cos x \) but will have a different structure.

**Hint:** Consider how the absolute value affects the graph of the cosine function.

### Step 3: Determine the modified period
The function \( | \cos x | \) will repeat itself every half cycle of the cosine function. Since \( \cos x \) has a period of \( 2\pi \), the absolute value function \( | \cos x | \) will repeat every \( \pi \) because the negative part of \( \cos x \) (from \( \pi \) to \( 2\pi \)) will be the same as the positive part (from \( 0 \) to \( \pi \)).

**Hint:** Think about the intervals where the cosine function is positive and negative.

### Step 4: Conclusion
Thus, the period of \( | \cos x | \) is \( \pi \).

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