Radians and Degrees: Definition & Examples

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  • 0:02 Importance of Degrees…
  • 0:56 What Are Degrees?
  • 1:38 What Are Radians?
  • 2:22 Converting Degress & Radians
  • 3:30 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

Radians and degrees are two ways of measuring angles. In this lesson, you will learn the definition of each method, see how to convert from one to the other and work some practice problems. There is also a quiz at the end of the lesson.

Importance of Degrees and Radians

Degrees and radians are the two main ways to measure angles. There are others, but these are the two that are most common. You might be thinking, 'why do we need two or more different ways to measure angles? What's wrong with just using degrees?' The answer might not seem clear at first, but the answer has to do with math. You can only do math with real numbers, and degrees are not actually numbers. They are conceptual, like percents. You can't solve a math problem like 'What is 25% of 44?' without first converting the percent to a decimal. 25% = 0.25

Then you can solve the problem.

0.25 x 44 = 11

The same is true with degrees. In order to solve mathematical problems, especially in higher math, such as Calculus, degrees must first be converted to radians.

What Are Degrees?

Degrees are used to measure direction and angle size. If you are facing north, you are said to be at 0°. If you turn the opposite direction to face south, you have turned 180°.

A full circle is comprised of 360°.

It is thought that this system of measuring circles was devised by the ancient Babylonians and was based on their sexagesimal system of counting. This system has 60 as its base compared to our current counting system with 10 as its base.

Most mathematical calculations up through Geometry use degrees to measure and calculate angles. There are many practical applications in building and architecture that use degree measures.

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