What is the area of a sector when 0 = 85° and r = 2 ? [ ? ]T
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°.
Related questions
Question
![**Question:** What is the area of a sector when \( \theta = 85^\circ \) and \( r = 2 \)?
**Diagram Explanation:**
The image shows a mathematical expression to find the area of a sector. A blank green square is in the numerator, which will contain a value multiplied by \( \pi \). There is a blank grey square in the denominator, indicating a value to divide by.
The formula for the area of a sector is:
\[ \text{Area} = \frac{\theta}{360^\circ} \times \pi r^2 \]
Using the given values:
- \( \theta = 85^\circ \)
- \( r = 2 \)
Plug these into the formula:
\[ \text{Area} = \frac{85}{360} \times \pi \times 2^2 \]
\[ \text{Area} = \frac{85}{360} \times \pi \times 4 \]
\[ \text{Area} = \frac{340}{360} \times \pi \]
\[ \text{Area} = \frac{17}{18} \times \pi \]
So, the area of the sector is \(\frac{17}{18} \pi\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e6f454-aef3-4078-bf5c-8f7a3cacb5c5%2Fc0371bcc-723e-4b17-bf00-fed3900c1a9a%2Fjwr0t4k_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:** What is the area of a sector when \( \theta = 85^\circ \) and \( r = 2 \)?
**Diagram Explanation:**
The image shows a mathematical expression to find the area of a sector. A blank green square is in the numerator, which will contain a value multiplied by \( \pi \). There is a blank grey square in the denominator, indicating a value to divide by.
The formula for the area of a sector is:
\[ \text{Area} = \frac{\theta}{360^\circ} \times \pi r^2 \]
Using the given values:
- \( \theta = 85^\circ \)
- \( r = 2 \)
Plug these into the formula:
\[ \text{Area} = \frac{85}{360} \times \pi \times 2^2 \]
\[ \text{Area} = \frac{85}{360} \times \pi \times 4 \]
\[ \text{Area} = \frac{340}{360} \times \pi \]
\[ \text{Area} = \frac{17}{18} \times \pi \]
So, the area of the sector is \(\frac{17}{18} \pi\).
Expert Solution
Step 1
Explanation of the answer is as follows
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning