Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To solve the problem, we need to determine the radian measure of a central angle corresponding to an arc measuring [tex]\(250^\circ\)[/tex]. Let's break down the steps in the solution:
1. Convert the angle from degrees to radians:
To convert an angle from degrees to radians, we use the fact that [tex]\(180^\circ = \pi\)[/tex] radians. Therefore, the conversion formula is:
[tex]\[ \text{Angle in Radians} = \text{Angle in Degrees} \times \frac{\pi}{180^\circ} \][/tex]
For [tex]\(250^\circ\)[/tex]:
[tex]\[ \text{Angle in Radians} = 250^\circ \times \frac{\pi}{180^\circ} \approx 4.3633 \ \text{radians} \][/tex]
2. Determine the range of the radian measure:
Compare the radian measure with the given ranges:
- [tex]\(0\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] radians is approximately [tex]\(0\)[/tex] to [tex]\(1.5708\)[/tex],
- [tex]\(\frac{\pi}{2}\)[/tex] to [tex]\(\pi\)[/tex] radians is approximately [tex]\(1.5708\)[/tex] to [tex]\(3.1416\)[/tex],
- [tex]\(\pi\)[/tex] to [tex]\(\frac{3\pi}{2}\)[/tex] radians is approximately [tex]\(3.1416\)[/tex] to [tex]\(4.7124\)[/tex],
- [tex]\(\frac{3\pi}{2}\)[/tex] to [tex]\(2\pi\)[/tex] radians is approximately [tex]\(4.7124\)[/tex] to [tex]\(6.2832\)[/tex].
Since [tex]\(4.3633 \ \text{radians}\)[/tex] falls between [tex]\(3.1416\)[/tex] and [tex]\(4.7124\)[/tex] radians, it is in the third range.
Therefore, the radian measure of the central angle falls within the range [tex]\(\pi\)[/tex] to [tex]\(\frac{3\pi}{2}\)[/tex] radians.
1. Convert the angle from degrees to radians:
To convert an angle from degrees to radians, we use the fact that [tex]\(180^\circ = \pi\)[/tex] radians. Therefore, the conversion formula is:
[tex]\[ \text{Angle in Radians} = \text{Angle in Degrees} \times \frac{\pi}{180^\circ} \][/tex]
For [tex]\(250^\circ\)[/tex]:
[tex]\[ \text{Angle in Radians} = 250^\circ \times \frac{\pi}{180^\circ} \approx 4.3633 \ \text{radians} \][/tex]
2. Determine the range of the radian measure:
Compare the radian measure with the given ranges:
- [tex]\(0\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] radians is approximately [tex]\(0\)[/tex] to [tex]\(1.5708\)[/tex],
- [tex]\(\frac{\pi}{2}\)[/tex] to [tex]\(\pi\)[/tex] radians is approximately [tex]\(1.5708\)[/tex] to [tex]\(3.1416\)[/tex],
- [tex]\(\pi\)[/tex] to [tex]\(\frac{3\pi}{2}\)[/tex] radians is approximately [tex]\(3.1416\)[/tex] to [tex]\(4.7124\)[/tex],
- [tex]\(\frac{3\pi}{2}\)[/tex] to [tex]\(2\pi\)[/tex] radians is approximately [tex]\(4.7124\)[/tex] to [tex]\(6.2832\)[/tex].
Since [tex]\(4.3633 \ \text{radians}\)[/tex] falls between [tex]\(3.1416\)[/tex] and [tex]\(4.7124\)[/tex] radians, it is in the third range.
Therefore, the radian measure of the central angle falls within the range [tex]\(\pi\)[/tex] to [tex]\(\frac{3\pi}{2}\)[/tex] radians.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.