What is Radian Measure in Geometry?

 When you learn about angles for the first time, you usually talk about them in terms of "degrees." You probably know what a 45-degree angle looks like. Also, by middle school, you know that a triangle has 180 degrees. It's simple, clear, and obvious. But most of today's great scientists prefer to use radians to measure angles.

 Now, you might ask, "Why radians?" It's not hard to get a degree, right?

 The History of Radians

 Back in the Middle Ages, the first mathematicians used the parts of a full circle to figure out how big a degree was. One degree is the same as one 360th of a circle. Even though there is no real reason why a circle has 360°, you have to accept it and move on.

360 is a great number, no matter what the reason is. This is because it is easy to divide by many other numbers: 180, 120, 90, 72, 60, 45, 40, 36, 24, 18, 15, 12, 10, 9, 8, 6, 5, 4, 3, and 2. The first ways to measure distance and time were based on using easy-to-understand numbers.

 Bring out the Radian

 Since the radian isn't a whole number, it isn't as easy and nice to work with. Some people think that radians were made so that mathematicians could figure out how to relate the size of a circle to the size of an angle.

 A radian is a lot bigger than a degree. The number of radians in a circle is 2, which is just a little more than six radians. One radian equals one-sixth of a circle, or slightly more than 57°.

 Why Do You Use Radians?

 The best thing about radians is that they are the natural way to divide a circle into parts. If you take the radius of a circle and bend it into an arc that lies on the circumference, you would need just over six of those to go all the way around the circle. This is a fact that is true in all circles.

 Converting between Degrees and Radians

 There is a simple formula to use if you have degrees and want to convert them to radians:

radians, which adds up to about 0.017D radians.

 If you have radians and want to convert them to degrees, you can use the following formula:

• degrees, which is about the same as 57.3R degrees
•  You don't have to remember these formulas, which is good news. Most calculators have functions that let you switch between degrees and radians and back again. This will make it easier to "come full circle" when solving hard math problems.

 Favorite Radians

 Angles that are a multiple of 15 degrees, like 90, 60, 45, and 30, are the most common or most liked. Because of the skill of early mathematicians (or just luck, we can't be sure), it's easy to turn these angles into radians. For example, 90° angles are equivalent to π/2; 60° angles are equivalent to π/3 radians; 45° angles are equivalent to π/4 radians; and 30° angles are equivalent to π/6 radians. Most of the time, radian measures with denominators of six, four, three, or two are used.

 You are now ready to use radians. With the information in this article, you are well on your way to joining the math elite.