Find the exact length of the arc intercepted by a central angle 0 on a circle of radius r. Then round to the nearest tenth of a unit. 0=330°, r= 13 in Part: 0/2 Part 1 of 2 The exact length of the arc is A X S Part: 1/2 Part 2 of 2 The approximate length of the arc, rounded to the nearest tenth of an inch, is S in. in.
Find the exact length of the arc intercepted by a central angle 0 on a circle of radius r. Then round to the nearest tenth of a unit. 0=330°, r= 13 in Part: 0/2 Part 1 of 2 The exact length of the arc is A X S Part: 1/2 Part 2 of 2 The approximate length of the arc, rounded to the nearest tenth of an inch, is S in. in.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![### Calculation of Arc Length
To find the exact length of the arc intercepted by a central angle \( \theta \) on a circle of radius \( r \), follow the given problem and steps. Then, round the answer to the nearest tenth of a unit.
Given:
- \( \theta = 330^\circ \)
- \( r = 13 \, \text{in} \)
#### Part 1 of 2
**The exact length of the arc is:** ______ in.
The response options provided are:
- \( \pi \)
- \( \square \)
- \( \square \)
- \( \times \)
- \( \circlearrowright \)
#### Part 2 of 2
**The approximate length of the arc, rounded to the nearest tenth of an inch, is:** ______ in.
The response options are:
- \( \times \)
- \( \circlearrowright \)
---
To proceed with solving the problem:
1. Use the formula for the arc length:
\[
s = r \theta
\]
Here, \( \theta \) needs to be in radians. Convert \( \theta \) from degrees to radians:
\[
\theta \, (\text{radians}) = \theta \, (\text{degrees}) \times \frac{\pi}{180^\circ}
\]
2. Thus:
\[
\theta \, (\text{radians}) = 330^\circ \times \frac{\pi}{180^\circ} = \frac{330 \pi}{180} = \frac{11 \pi}{6}
\]
3. Substitute the values into the arc length formula:
\[
s = r \times \theta = 13 \, \text{in} \times \frac{11\pi}{6}
\]
4. Calculate the exact length:
\[
s = \frac{143 \pi}{6} \, \text{in}
\]
5. To find the approximate length, calculate:
\[
s \approx \frac{143 \times 3.14}{6} = 74.78 \approx 74.8 \, \text{in}
\]
These are the steps that need to be followed and can be done interactively for better understanding. The exact length can be expressed in terms of \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9ae2b74-0627-461f-a855-f05238f3c436%2F3cb5ea4c-0746-4feb-a988-ade83364e595%2Fj9640mk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculation of Arc Length
To find the exact length of the arc intercepted by a central angle \( \theta \) on a circle of radius \( r \), follow the given problem and steps. Then, round the answer to the nearest tenth of a unit.
Given:
- \( \theta = 330^\circ \)
- \( r = 13 \, \text{in} \)
#### Part 1 of 2
**The exact length of the arc is:** ______ in.
The response options provided are:
- \( \pi \)
- \( \square \)
- \( \square \)
- \( \times \)
- \( \circlearrowright \)
#### Part 2 of 2
**The approximate length of the arc, rounded to the nearest tenth of an inch, is:** ______ in.
The response options are:
- \( \times \)
- \( \circlearrowright \)
---
To proceed with solving the problem:
1. Use the formula for the arc length:
\[
s = r \theta
\]
Here, \( \theta \) needs to be in radians. Convert \( \theta \) from degrees to radians:
\[
\theta \, (\text{radians}) = \theta \, (\text{degrees}) \times \frac{\pi}{180^\circ}
\]
2. Thus:
\[
\theta \, (\text{radians}) = 330^\circ \times \frac{\pi}{180^\circ} = \frac{330 \pi}{180} = \frac{11 \pi}{6}
\]
3. Substitute the values into the arc length formula:
\[
s = r \times \theta = 13 \, \text{in} \times \frac{11\pi}{6}
\]
4. Calculate the exact length:
\[
s = \frac{143 \pi}{6} \, \text{in}
\]
5. To find the approximate length, calculate:
\[
s \approx \frac{143 \times 3.14}{6} = 74.78 \approx 74.8 \, \text{in}
\]
These are the steps that need to be followed and can be done interactively for better understanding. The exact length can be expressed in terms of \(
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