To determine how many \(\pi\) radians are equivalent to \(3600^\circ\), we can use the fact that \(180^\circ = \pi\) radians.

### Conversion Formula:
\[
\text{Radians} = \frac{\pi}{180^\circ} \times \text{Degrees}
\]

Substituting \(3600^\circ\) into the formula:

\[
\text{Radians} = \frac{\pi}{180^\circ} \times 3600^\circ = 20\pi \text{ radians}
\]

So, \(3600^\circ\) equals \(20\pi\) radians.

Would you like more details or have any other questions? Here are some related questions:

1. How do you convert from radians to degrees?
2. What is the radian measure of a full circle (360°)?
3. How many radians are in half a circle (180°)?
4. How can you simplify radian conversions for common angles?
5. What are the applications of radians in trigonometry?

**Tip:** When converting angles, remember that \( \pi \) radians is equivalent to \(180^\circ\).

Learn how to convert 3600° to radians using the formula Radians = (π / 180°) × Degrees. Understand the relationship between degrees and radians with this detailed, step-by-step solution. Suitable for high school students in Grades 9-12.

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