IDNLearn.com offers a collaborative platform for sharing and gaining knowledge. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.
Sagot :
To determine the radian measure of the central angle for an arc CD, which is [tex]\(\frac{1}{4}\)[/tex] of the circumference of a circle, let's follow these steps:
1. Understand the relationship between arc length and the central angle:
- The circumference of the entire circle is [tex]\(2\pi\)[/tex] radians in terms of the central angle.
- Given that arc CD is [tex]\(\frac{1}{4}\)[/tex] of the total circumference, the central angle corresponding to arc CD will be [tex]\(\frac{1}{4}\)[/tex] of the full circle's central angle.
2. Calculate the central angle in radians:
- Since the full circle in radians is [tex]\(2\pi\)[/tex],
- The central angle corresponding to arc CD is [tex]\(\frac{1}{4} \times 2\pi\)[/tex].
3. Perform the fraction multiplication:
- [tex]\(\frac{1}{4} \times 2\pi = \frac{2\pi}{4} = \frac{\pi}{2}\)[/tex].
So, the radian measure of the central angle corresponding to arc CD, which is [tex]\(\frac{1}{4}\)[/tex] of the circumference of the circle, is [tex]\(\frac{\pi}{2}\)[/tex] radians.
Hence, the correct answer is [tex]\(\frac{\pi}{2}\)[/tex] radians.
1. Understand the relationship between arc length and the central angle:
- The circumference of the entire circle is [tex]\(2\pi\)[/tex] radians in terms of the central angle.
- Given that arc CD is [tex]\(\frac{1}{4}\)[/tex] of the total circumference, the central angle corresponding to arc CD will be [tex]\(\frac{1}{4}\)[/tex] of the full circle's central angle.
2. Calculate the central angle in radians:
- Since the full circle in radians is [tex]\(2\pi\)[/tex],
- The central angle corresponding to arc CD is [tex]\(\frac{1}{4} \times 2\pi\)[/tex].
3. Perform the fraction multiplication:
- [tex]\(\frac{1}{4} \times 2\pi = \frac{2\pi}{4} = \frac{\pi}{2}\)[/tex].
So, the radian measure of the central angle corresponding to arc CD, which is [tex]\(\frac{1}{4}\)[/tex] of the circumference of the circle, is [tex]\(\frac{\pi}{2}\)[/tex] radians.
Hence, the correct answer is [tex]\(\frac{\pi}{2}\)[/tex] radians.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.