Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine the range of the central angle of an arc that measures [tex]\(295^\circ\)[/tex] when converted to radians, follow these steps:
1. Convert angles from degrees to radians:
- The formula to convert degrees to radians is:
[tex]\[ \text{angle in radians} = \text{angle in degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
- Applying this formula:
[tex]\[ 295^\circ \times \left(\frac{\pi}{180}\right) = 5.1487212933832724 \text{ radians} \][/tex]
2. Determine the range of the angle in radians:
- We need to see within which of the following ranges [tex]\(5.1487212933832724\)[/tex] radians falls:
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
3. Evaluate the boundaries of these ranges:
[tex]\[ \begin{align*} 0 & \leq \text{angle} < \frac{\pi}{2} \quad \text{(approximately } 0 \leq \text{angle} < 1.5708) \\ \frac{\pi}{2} & \leq \text{angle} < \pi \quad \text{(approximately } 1.5708 \leq \text{angle} < 3.1416) \\ \pi & \leq \text{angle} < \frac{3\pi}{2} \quad \text{(approximately } 3.1416 \leq \text{angle} < 4.7124) \\ \frac{3\pi}{2} & \leq \text{angle} \leq 2\pi \quad \text{(approximately } 4.7124 \leq \text{angle} \leq 6.2832) \\ \end{align*} \][/tex]
4. Compare the angle [tex]\(5.1487212933832724\)[/tex] radians with these ranges:
[tex]\(5.1487212933832724\)[/tex] radians is greater than [tex]\(4.7124\)[/tex] but less than [tex]\(6.2832\)[/tex].
Therefore, the central angle of [tex]\(295^\circ\)[/tex] (or [tex]\(5.1487212933832724\)[/tex] radians) falls within the range:
[tex]\[ \frac{3\pi}{2} \text{ to } 2\pi \text{ radians} \][/tex]
1. Convert angles from degrees to radians:
- The formula to convert degrees to radians is:
[tex]\[ \text{angle in radians} = \text{angle in degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
- Applying this formula:
[tex]\[ 295^\circ \times \left(\frac{\pi}{180}\right) = 5.1487212933832724 \text{ radians} \][/tex]
2. Determine the range of the angle in radians:
- We need to see within which of the following ranges [tex]\(5.1487212933832724\)[/tex] radians falls:
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
3. Evaluate the boundaries of these ranges:
[tex]\[ \begin{align*} 0 & \leq \text{angle} < \frac{\pi}{2} \quad \text{(approximately } 0 \leq \text{angle} < 1.5708) \\ \frac{\pi}{2} & \leq \text{angle} < \pi \quad \text{(approximately } 1.5708 \leq \text{angle} < 3.1416) \\ \pi & \leq \text{angle} < \frac{3\pi}{2} \quad \text{(approximately } 3.1416 \leq \text{angle} < 4.7124) \\ \frac{3\pi}{2} & \leq \text{angle} \leq 2\pi \quad \text{(approximately } 4.7124 \leq \text{angle} \leq 6.2832) \\ \end{align*} \][/tex]
4. Compare the angle [tex]\(5.1487212933832724\)[/tex] radians with these ranges:
[tex]\(5.1487212933832724\)[/tex] radians is greater than [tex]\(4.7124\)[/tex] but less than [tex]\(6.2832\)[/tex].
Therefore, the central angle of [tex]\(295^\circ\)[/tex] (or [tex]\(5.1487212933832724\)[/tex] radians) falls within the range:
[tex]\[ \frac{3\pi}{2} \text{ to } 2\pi \text{ radians} \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.