IDNLearn.com: Your trusted platform for finding reliable answers. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.
An arc on a circle measures [tex]\(250^{\circ}\)[/tex]. Within which range is the radian measure of the central angle?
A. [tex]\(0\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] radians B. [tex]\(\frac{\pi}{2}\)[/tex] to [tex]\(\pi\)[/tex] radians C. [tex]\(\pi\)[/tex] to [tex]\(\frac{3\pi}{2}\)[/tex] radians D. [tex]\(\frac{3\pi}{2}\)[/tex] to [tex]\(2\pi\)[/tex] radians
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.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.
