Write the interval in which the function `f(x)=cos x` is strictly decreasing.

Answer

To determine the interval in which the function \( f(x) = \cos x \) is strictly decreasing, we will follow these steps:

### Step 1: Find the derivative of the function
The first step is to find the derivative of the function \( f(x) = \cos x \).

\[ f'(x) = -\sin x \]

### Step 2: Determine where the derivative is negative
The function \( f(x) \) is strictly decreasing where its derivative \( f'(x) \) is less than zero.

\[ -\sin x < 0 \]

This simplifies to:

\[ \sin x > 0 \]

### Step 3: Identify the intervals where \( \sin x > 0 \)
The sine function is positive in the intervals:

- \( (0, \pi) \)
- \( (2\pi, 3\pi) \)
- \( (4\pi, 5\pi) \)
- and so on...

In general, this can be expressed as:

\[ x \in (2n\pi, (2n + 1)\pi) \quad \text{for integers } n \]

### Step 4: Write the final answer
Thus, the intervals in which the function \( f(x) = \cos x \) is strictly decreasing are:

\[ (2n\pi, (2n + 1)\pi) \quad \text{for } n \in \mathbb{Z} \]

### Summary of the intervals
- For \( n = 0 \): \( (0, \pi) \)
- For \( n = 1 \): \( (2\pi, 3\pi) \)
- For \( n = -1 \): \( (-2\pi, -\pi) \)