with a length of exactly 24pi/7 what how many radians is angle atheta

If the arc length of a circle is \( s = \frac{24\pi}{7} \) and you're asked to find the corresponding angle in radians (\(\theta\)), you can use the formula for arc length:

\[
s = r\theta
\]

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

However, if the radius \( r \) is not given, we would assume the formula applies directly to the unit circle, where \( r = 1 \). In that case, the formula simplifies to:

\[
s = \theta
\]

Therefore, for a radius of 1, the angle \( \theta \) would be:

\[
\theta = \frac{24\pi}{7}
\]

Thus, the angle in radians is \( \frac{24\pi}{7} \).

### Would you like to see further details on arc length and radians?

Here are some related questions:

1. How is the formula for arc length derived?
2. What is the relationship between degrees and radians?
3. How do you convert a given angle in degrees to radians?
4. How does the arc length change with different radii?
5. What is the angle in degrees if \( \theta = \frac{24\pi}{7} \)?

**Tip**: On the unit circle, the arc length is always equal to the angle in radians!

Explore how to find the angle in radians when the arc length is 24π/7 using the formula s = rθ. This problem involves core concepts from trigonometry and geometry, ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation