What is the area of a sector 2 and 0 = 1.75 radians? when r
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 \( r = 2 \) and \( \theta = 1.75 \) radians?
\[ \begin{bmatrix} ? \end{bmatrix} \]
*Note*: Put your answer in decimal form.
---
**Explanation**:
To find the area of a sector, use the formula:
\[
\text{Area} = \frac{1}{2} r^2 \theta
\]
Where:
- \( r \) is the radius of the circle.
- \( \theta \) is the angle in radians.
In this case:
- \( r = 2 \)
- \( \theta = 1.75 \)
Substitute the values into the formula:
\[
\text{Area} = \frac{1}{2} (2)^2 (1.75) = 2(1.75) = 3.5
\]
Therefore, the area of the sector is 3.5 square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e6f454-aef3-4078-bf5c-8f7a3cacb5c5%2F90a27c1e-ed71-47e6-8894-65ad7699f482%2Fk7ird3_processed.png&w=3840&q=75)
Transcribed Image Text:**Question**: What is the area of a sector when \( r = 2 \) and \( \theta = 1.75 \) radians?
\[ \begin{bmatrix} ? \end{bmatrix} \]
*Note*: Put your answer in decimal form.
---
**Explanation**:
To find the area of a sector, use the formula:
\[
\text{Area} = \frac{1}{2} r^2 \theta
\]
Where:
- \( r \) is the radius of the circle.
- \( \theta \) is the angle in radians.
In this case:
- \( r = 2 \)
- \( \theta = 1.75 \)
Substitute the values into the formula:
\[
\text{Area} = \frac{1}{2} (2)^2 (1.75) = 2(1.75) = 3.5
\]
Therefore, the area of the sector is 3.5 square units.
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