IDNLearn.com: Where your questions are met with thoughtful and precise answers. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.

Arc CD is [tex]\frac{1}{4}[/tex] of the circumference of a circle. What is the radian measure of the central angle?

A. [tex]\frac{\pi}{4}[/tex] radians
B. [tex]\frac{\pi}{2}[/tex] radians
C. [tex]2\pi[/tex] radians
D. [tex]4\pi[/tex] radians


Sagot :

To determine the radian measure of the central angle corresponding to arc CD, we need to understand the relationship between the arc length and the central angle.

Given:
- Arc CD is [tex]\(\frac{1}{4}\)[/tex] of the circumference of the circle.

First, recall that the circumference of a circle is given by [tex]\(C = 2\pi r\)[/tex], where [tex]\(r\)[/tex] is the radius. The entire circumference corresponds to a central angle of [tex]\(2\pi\)[/tex] radians.

Since arc CD is [tex]\(\frac{1}{4}\)[/tex] of the circumference, the central angle corresponding to arc CD will be [tex]\(\frac{1}{4}\)[/tex] of [tex]\(2\pi\)[/tex] radians.

To find this angle, we calculate:
[tex]\[ \text{Central angle} = \frac{1}{4} \times 2\pi \][/tex]

By simplifying the product:
[tex]\[ \text{Central angle} = \frac{1}{4} \times 2\pi = \frac{2\pi}{4} = \frac{\pi}{2} \][/tex]

Therefore, the radian measure of the central angle is:

[tex]\[ \boxed{\frac{\pi}{2}} \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.