How far does the tip of a 1.39 m pendulum travel as it swings through an angle of 6.3°? The distance through which the end of the pendulum swings is m. (Simplify your answer. Round to three decimal places as needed.)
How far does the tip of a 1.39 m pendulum travel as it swings through an angle of 6.3°? The distance through which the end of the pendulum swings is m. (Simplify your answer. Round to three decimal places as needed.)
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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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![**Pendulum Swing Distance Calculation**
**Problem Statement**:
How far does the tip of a 1.39 m pendulum travel as it swings through an angle of 6.3°?
**Solution**:
The distance through which the end of the pendulum swings is _______ m.
(Simplify your answer. Round to three decimal places as needed.)
**Explanation**:
To find the distance that the tip of the pendulum travels, we need to calculate the arc length. The arc length \( S \) of a circle is given by the formula:
\[ S = r \cdot \theta \]
where:
- \( r \) is the radius (length of the pendulum in this case), and
- \( \theta \) is the angle in radians.
To convert the angle from degrees to radians, use:
\[ \theta \, (\text{in radians}) = \theta \, (\text{in degrees}) \times \frac{\pi}{180} \]
Substitute the given values (\( r = 1.39 \) m, \( \theta = 6.3^\circ \)) into the formulas to find the arc length.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb5c4afe-031f-4485-8b26-650e5f71f638%2Fd8063c40-12ee-4833-84df-fd78723d28a1%2Fsnrd7h_processed.png&w=3840&q=75)
Transcribed Image Text:**Pendulum Swing Distance Calculation**
**Problem Statement**:
How far does the tip of a 1.39 m pendulum travel as it swings through an angle of 6.3°?
**Solution**:
The distance through which the end of the pendulum swings is _______ m.
(Simplify your answer. Round to three decimal places as needed.)
**Explanation**:
To find the distance that the tip of the pendulum travels, we need to calculate the arc length. The arc length \( S \) of a circle is given by the formula:
\[ S = r \cdot \theta \]
where:
- \( r \) is the radius (length of the pendulum in this case), and
- \( \theta \) is the angle in radians.
To convert the angle from degrees to radians, use:
\[ \theta \, (\text{in radians}) = \theta \, (\text{in degrees}) \times \frac{\pi}{180} \]
Substitute the given values (\( r = 1.39 \) m, \( \theta = 6.3^\circ \)) into the formulas to find the arc length.
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