IDNLearn.com provides a comprehensive solution for all your question and answer needs. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.
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 value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.