Find the exact length of the arc intercepted by the given central angle in the figure to the right.
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Part 1
StartFraction 7 pi Over 4 EndFraction
7π
4


To find the exact length of the arc intercepted by a given central angle, we use the formula for the arc length:

\[
s = r \theta
\]

where:
- \( s \) is the arc length,
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.

Given:
- Central angle \( \theta = \frac{7\pi}{4} \).

If the radius \( r \) is not provided, we cannot find the exact arc length. Assuming you have a specific radius value from the figure to the right, plug it into the formula.

### Example Calculation:
If the radius is \( r = 1 \) (unit circle assumption), then:
\[
s = 1 \times \frac{7\pi}{4} = \frac{7\pi}{4}
\]

If the radius is something else, say \( r = 2 \), then:
\[
s = 2 \times \frac{7\pi}{4} = \frac{7\pi}{2}
\]

Please provide the radius if you need a more specific answer.

Do you want more details, or have any questions about this? Here are some related questions:

1. How does the arc length formula change if the angle is in degrees?
2. What is the relationship between arc length and the circumference of a circle?
3. How can we derive the formula for arc length from the circumference formula?
4. What would be the arc length for a central angle of \( \pi \) radians in a circle with radius 5?
5. How does changing the radius of a circle affect the arc length?

**Tip:** Always ensure the angle is in radians when using the arc length formula \( s = r \theta \). If given in degrees, convert to radians first.

Find the exact length of the arc intercepted by the given central angle in the figure to the right.
Part 1
StartFraction 7 pi Over 4 EndFraction

Learn how to calculate the exact arc length intercepted by a central angle of 7π/4 radians. This problem involves using the arc length formula s = rθ and understanding the relationship between the radius and the central angle in radians. Suitable for high school students (Grades 9-12).

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