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Converting degrees to radians is a fundamental concept in trigonometry that allows us to express angles in a unit that is commonly used in mathematics and physics. Radians provide a more natural and convenient way to measure angles, especially when dealing with circular and periodic phenomena. This topic explores the relationship between degrees and radians, and provides step-by-step instructions on how to convert between the two units. Understanding this conversion is essential for solving trigonometric equations, working with circular functions, and analyzing the behavior of waves and oscillations. So, let’s dive into the world of degrees and radians and discover how to convert between them efficiently and accurately.
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Degrees and radians are two units of angle measurement. ^{[1] X Research Source} A circle has 360 degrees, which is equivalent to 2π radians, so 360° and 2π radians represent the numerical value of “one turn” of the circle. ^{[2] X Research Source} If you’re still confused don’t worry, with just a few simple steps you can easily convert degrees to radians and vice versa.
Steps
- Example 1 : 120°
- Example 2 : 30°
- Example 3 : 225°
- Example 1 : 120 x /180
- Example 2 : 30 x /180
- Example 3 : 225 x /180
- Example 1 : 120 x /180 = 120π/180
- Example 2 : 30 x /180 = 30π/180
- Example 3 : 225 x /180 = 225π/180
- Example 1 : 120 x /180 = 120π/180 60/60 = 2/3π radians
- Example 2 : 30 x /180 = 30π/180 30/30 = 1/6π radian
- Example 3 : 225 x /180 = 225π/180 45/45 = 5/4π radians
- Example 1 : 120° = 2/3π radian
- Example 2 : 30° = 1/6π radian
- Example 3 : 225° = 5/4π radian
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, volunteer authors have edited and improved the article over time.
There are 7 references cited in this article that you can view at the bottom of the page.
This article has been viewed 235,170 times.
Degrees and radians are two units of angle measurement. ^{[1] X Research Source} A circle has 360 degrees, which is equivalent to 2π radians, so 360° and 2π radians represent the numerical value of “one turn” of the circle. ^{[2] X Research Source} If you’re still confused don’t worry, with just a few simple steps you can easily convert degrees to radians and vice versa.
In conclusion, converting degrees to radians is a simple process that involves multiplying the degree measure by the conversion factor of π/180. This conversion is necessary when dealing with trigonometric functions or when working with radian-based calculations. By understanding the relationship between degrees and radians and following the steps outlined in this article, anyone can easily convert measurements from degrees to radians with accuracy and confidence. Remembering the key formula and practicing with various examples will help solidify the concept and enable smooth conversion in any mathematical or scientific scenario.
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