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The problem is asking to solve the equation:

\[
\cos(x) = 1 \quad \text{for} \quad 0^\circ \leq x \leq 360^\circ.
\]

### Solution:

The cosine function equals 1 at specific values of \( x \). Within the interval \( [0^\circ, 360^\circ] \), cosine equals 1 only at \( x = 0^\circ \) and \( x = 360^\circ \) because:

\[
\cos(0^\circ) = 1 \quad \text{and} \quad \cos(360^\circ) = 1.
\]

Therefore, the solutions are:

\[
x = 0^\circ \quad \text{and} \quad x = 360^\circ.
\]

Would you like further explanation on this? 

Here are five related questions you might find interesting:
1. What is the general solution for \( \cos(x) = 1 \) for all \( x \)?
2. At which angles does \( \cos(x) = 0 \) between 0° and 360°?
3. Can you describe the graph of the cosine function between 0° and 360°?
4. What are the solutions for \( \sin(x) = 1 \) for the same range of \( x \)?
5. What is the relationship between \( \cos(x) \) and \( \sin(x) \) for various values of \( x \)?

**Tip:** For trigonometric equations, it helps to visualize the unit circle, as it quickly reveals where sine and cosine take on specific values.

Solve the equation cos(x) = 1 for 0° ≤ x ≤ 360°.

Learn how to solve the trigonometric equation cos(x) = 1 within the range 0° to 360°. The solution highlights key trigonometric concepts like the cosine function and angle measurement. Suitable for students in Grades 9-12.

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