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Chapter 13: Problem 60

Express \(\frac{1}{8}\) of a revolution in degrees.

Short Answer

Expert verified
\(\frac{1}{8}\) of a revolution is 45 degrees.

Step by step solution

01

Understand the Problem

We need to find out how many degrees correspond to \(\frac{1}{8}\) of a full revolution. A full revolution is equal to 360 degrees.
02

Set Up the Proportion

To find \(\frac{1}{8}\) of a revolution in degrees, we can express it as \(\frac{1}{8} \times 360\).
03

Perform the Calculation

Calculate \(\frac{1}{8} \times 360\) by dividing 360 by 8.\[\frac{360}{8} = 45\]
04

Conclude the Calculation

Therefore, \(\frac{1}{8}\) of a revolution is equivalent to 45 degrees.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Full Revolution
A full revolution is the term we use when an object completes one complete turn around a circle. It is the basic unit of rotation measurement in circles and is universally accepted to equal 360 degrees.
Understanding what a full revolution means is crucial for converting between different units of angle measurement.
When an object goes through a complete turn, it has traveled the full 360 degrees. This concept underpins the way we think about circles and angles, making it an essential part of geometry, trigonometry, and even everyday applications like telling time on an analog clock.
Proportion
Proportion helps us compare parts of a whole with its entirety. In the context of angles, a proportion can relate a portion of a revolution to the complete revolution through a simple mathematical relationship.
For example, if we have \(\frac{1}{8}\) of a revolution, we are looking at one eighth of the whole 360 degrees.
By setting up a proportion, such as \(\frac{1}{8} \) of 360, we can identify the number of degrees present in that particular fraction of the entire circle.
  • This method of using proportion is very effective in converting units or determining relationships between quantities.
  • It simplifies complex calculations, offering a straightforward path to find answers by focusing on the relation of parts to the whole.
Conversion from Revolutions to Degrees
The conversion from revolutions to degrees is a practical process used whenever we want to express a fraction of a revolution in degrees.
Since a full revolution equals 360 degrees, any fraction of a revolution can be transformed into degrees through multiplication.
Here is how you can convert from revolutions to degrees:
  • Identify the fraction of the revolution you want to convert.
  • Multiply this fraction by 360 (because 360 degrees makes a full revolution).
  • The product will be the equivalent number of degrees.
For instance, to convert \(\frac{1}{8}\) of a revolution to degrees, you multiply \(\frac{1}{8} \) by 360.
The calculation \(\frac{1}{8} \times 360 = 45\) reveals that \(\frac{1}{8}\) of a revolution equals 45 degrees.
This simple multiplication gives a direct way to find out how much of the circle you have covered in terms of degrees.

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