4. Find the zeros of the function $f(x)=\sqrt{1-\cos ^{2} 2 x}$ and sketch its graph on the interval $[-\pi, 2 \pi]$.

Solve the problems independently on the attached paper, and do so on a separate page for each problem.

Do not sign the sheets, write only your code.

Write your answers with a pen clearly and neatly. Each problem's solution will be graded on a scale from 0 to 6 points.
4. First, we write $f(x)=\sqrt{1-\cos ^{2} 2 x}=\sqrt{\sin ^{2} 2 x}=|\sin 2 x|$. The zeros of the function are $x=\frac{k \pi}{2}, k \in$ $\mathbb{Z}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-13.jpg?height=320&width=1056&top_left_y=1576&top_left_x=497)

We note: $f(x)=\sqrt{1-\cos ^{2} 2 x}=\sqrt{\sin ^{2} 2 x} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots 1$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-13.jpg?height=60&width=1642&top_left_y=1995&top_left_x=204)

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-13.jpg?height=65&width=1639&top_left_y=2052&top_left_x=206)

Zeros drawn on the graph .................................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-13.jpg?height=63&width=1642&top_left_y=2147&top_left_x=204)

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-13.jpg?height=63&width=1639&top_left_y=2196&top_left_x=206)