Find w for the minute hand of a clook.
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
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Can you please assist me with this homework problem in the image?
![**Solve the problem.**
Find \( \omega \) for the minute hand of a clock.
---
**Explanation:**
- \( \omega \) represents the angular velocity.
- The minute hand of a clock completes one full revolution (360 degrees or \(2\pi\) radians) in 60 minutes.
- To find \( \omega \), calculate the angular velocity in radians per minute.
The formula for angular velocity is:
\[ \omega = \frac{\text{angle in radians}}{\text{time in minutes}} \]
For the minute hand:
\[
\omega = \frac{2\pi \text{ radians}}{60 \text{ minutes}} = \frac{\pi}{30} \text{ radians per minute}
\]
Thus, the angular velocity \( \omega \) of the minute hand is \( \frac{\pi}{30} \) radians per minute.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4283f212-ef6a-42bb-9a98-bd2f9ea72575%2F434b59da-403c-423c-a3c0-774d2079ec8d%2Fjrki0a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the problem.**
Find \( \omega \) for the minute hand of a clock.
---
**Explanation:**
- \( \omega \) represents the angular velocity.
- The minute hand of a clock completes one full revolution (360 degrees or \(2\pi\) radians) in 60 minutes.
- To find \( \omega \), calculate the angular velocity in radians per minute.
The formula for angular velocity is:
\[ \omega = \frac{\text{angle in radians}}{\text{time in minutes}} \]
For the minute hand:
\[
\omega = \frac{2\pi \text{ radians}}{60 \text{ minutes}} = \frac{\pi}{30} \text{ radians per minute}
\]
Thus, the angular velocity \( \omega \) of the minute hand is \( \frac{\pi}{30} \) radians per minute.
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