IDNLearn.com offers a collaborative platform for sharing and gaining knowledge. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.
Sagot :
To determine which range the measure of the central angle falls in, we need to follow these steps:
1. Convert the Angle from Degrees to Radians:
- The given angle is [tex]\(85^\circ\)[/tex].
- To convert degrees to radians, use the conversion factor: [tex]\(1^\circ = \frac{\pi}{180}\)[/tex] radians.
- Therefore, [tex]\(85^\circ\)[/tex] can be converted to radians as follows:
[tex]\[ 85 \times \frac{\pi}{180} = \frac{85\pi}{180} \][/tex]
- Simplifying this, we get:
[tex]\[ \frac{85\pi}{180} = \frac{17\pi}{36} \][/tex]
- In decimal form, approximately:
[tex]\[ \frac{17\pi}{36} \approx 1.4835298641951802 \text{ radians} \][/tex]
2. Determine the Range:
- We need to identify the range in which [tex]\(1.4835298641951802\)[/tex] radians lies.
- The given ranges are:
1. [tex]\(0\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] radians
2. [tex]\(\frac{\pi}{2}\)[/tex] to [tex]\(\pi\)[/tex] radians
3. [tex]\(\pi\)[/tex] to [tex]\(\frac{3\pi}{2}\)[/tex] radians
4. [tex]\(\frac{3\pi}{2}\)[/tex] to [tex]\(2\pi\)[/tex] radians
- Let's compare [tex]\(1.4835298641951802\)[/tex] radians with the boundary values of these ranges.
- [tex]\(\frac{\pi}{2} \approx 1.5707963267948966\)[/tex] radians
- [tex]\(\pi \approx 3.141592653589793\)[/tex] radians
- [tex]\(\frac{3\pi}{2} \approx 4.71238898038469\)[/tex] radians
- [tex]\(2\pi \approx 6.283185307179586\)[/tex] radians
- Clearly,
[tex]\[ 0 \leq 1.4835298641951802 < 1.5707963267948966 \][/tex]
This shows that [tex]\(1.4835298641951802\)[/tex] radians falls in the first range.
Therefore, the measure of the central angle in radians lies within the range:
[tex]\[0 \text{ to } \frac{\pi}{2} \text{ radians}\][/tex]
Answer: 0 to [tex]\(\frac{\pi}{2}\)[/tex] radians.
1. Convert the Angle from Degrees to Radians:
- The given angle is [tex]\(85^\circ\)[/tex].
- To convert degrees to radians, use the conversion factor: [tex]\(1^\circ = \frac{\pi}{180}\)[/tex] radians.
- Therefore, [tex]\(85^\circ\)[/tex] can be converted to radians as follows:
[tex]\[ 85 \times \frac{\pi}{180} = \frac{85\pi}{180} \][/tex]
- Simplifying this, we get:
[tex]\[ \frac{85\pi}{180} = \frac{17\pi}{36} \][/tex]
- In decimal form, approximately:
[tex]\[ \frac{17\pi}{36} \approx 1.4835298641951802 \text{ radians} \][/tex]
2. Determine the Range:
- We need to identify the range in which [tex]\(1.4835298641951802\)[/tex] radians lies.
- The given ranges are:
1. [tex]\(0\)[/tex] to [tex]\(\frac{\pi}{2}\)[/tex] radians
2. [tex]\(\frac{\pi}{2}\)[/tex] to [tex]\(\pi\)[/tex] radians
3. [tex]\(\pi\)[/tex] to [tex]\(\frac{3\pi}{2}\)[/tex] radians
4. [tex]\(\frac{3\pi}{2}\)[/tex] to [tex]\(2\pi\)[/tex] radians
- Let's compare [tex]\(1.4835298641951802\)[/tex] radians with the boundary values of these ranges.
- [tex]\(\frac{\pi}{2} \approx 1.5707963267948966\)[/tex] radians
- [tex]\(\pi \approx 3.141592653589793\)[/tex] radians
- [tex]\(\frac{3\pi}{2} \approx 4.71238898038469\)[/tex] radians
- [tex]\(2\pi \approx 6.283185307179586\)[/tex] radians
- Clearly,
[tex]\[ 0 \leq 1.4835298641951802 < 1.5707963267948966 \][/tex]
This shows that [tex]\(1.4835298641951802\)[/tex] radians falls in the first range.
Therefore, the measure of the central angle in radians lies within the range:
[tex]\[0 \text{ to } \frac{\pi}{2} \text{ radians}\][/tex]
Answer: 0 to [tex]\(\frac{\pi}{2}\)[/tex] radians.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.