Advantages of Radian Measurements

In summary: It just feels nice to work with.The Babylonians are thought to be the ones that started using degrees instead of radians. 360 is also a number that is easy to remember.
  • #1
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Hey,

Simple questions, and hopefully I can explain my query a bit better than others I have made. I'm just trying to think of any advantages for using radians instead of degrees? I know/think that degrees are an arbitrary unit but cannot think of any reasons for using 360.

1. What are the advantages of using radians?

2. If degrees are an arbitrary unit then, where did the number 360 come from? Is it some how related to time, with 60 being a multiple of 360.

3. Am I correct in saying that to convert 1 degree to radians I would use, 1 x π/180, and if converting 1 radian to degrees, I would use 1 x 180/π

Thanks.
 
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  • #2
Heuristically, if you have a definite radius of rotation, use radians; if you don't, use degrees. Thus, in rotating machinery, radian usage makes all the formulas much easier and, in surveying, degree usage makes the shots much easier.

As to why 360, many folks think the Babylonians are to blame. They used a base 60 number system. Others have noted that many ancient folks (and some modern ones) think 12 is a magical number.

I personally think gradients (that's the G in the DRG button of your calculator) got a bad rap and should be used more.

And, yes, your conversions are accurate.
 
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  • #3
Would it be true in saying that using radians is more specific to the actual circle you are measuring? As it is directly related to the circle, as it uses other parts of it, almost as a ration to determin it? Where as the degrees system is only reliant on dividing the circle into 360 pieces.

Am I correct in saying that to convert 1 degree to radians I would use, 1 x π/180, and if converting 1 radian to degrees, I would use 1 x 180/π
 
  • #4
Radians are nice because there are 2*pi of them in a circle, and 2*pi*r is the circumference of a circle... that means that you can multiply the number of radians in an angle by the radius to calculate the length of the arc for any slice of a circle, which turns out to be useful quite often in applied physics problems.
 
  • #5
360 is great number. and what makes it great is the fact that it is divisible by 2,3,4,5,6,8...(many small and useful numbers)
 
  • #6
Well I think I'll be using them quite soon both in mechanics and in physics, so it's nice to have a little head start thanks.
 
  • #7
Radians are required for trigonometric functions and calculus. For example
[tex]\frac{d}{dx}\sin{x^2} = 2x\cos{x^2}[/tex]
is only true if x is in radians.
 
  • #8
Yes, I think that we are moving onto more advanced trigonometry within the next few weeks, and I have also heard the teacher mention them.
 

1. What is a radian measurement?

A radian is a unit of measurement for angles, defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. It is represented by the symbol "rad" and is considered a standard unit in the International System of Units (SI).

2. What are the advantages of using radians instead of degrees?

Radians have several advantages over degrees when it comes to measuring angles. They are a more natural unit for calculating angles in trigonometric functions, making it easier to use them in mathematical calculations. Additionally, they eliminate the need for conversion factors in trigonometric equations, simplifying the process. Radians also have a more intuitive relationship with the circumference and area of a circle, making them useful in geometry and physics.

3. How are radians and degrees related?

Radians and degrees are two different units for measuring angles, but they are related by a conversion factor. One full rotation around a circle is equal to 360 degrees or 2π radians. This means that 1 radian is equal to approximately 57.3 degrees. To convert from radians to degrees, multiply the radian measure by 180/π, and to convert from degrees to radians, multiply the degree measure by π/180.

4. Are there any real-world applications of radians?

Yes, radians are commonly used in fields such as physics, engineering, and mathematics. They are particularly useful in fields that involve circular motion, such as calculating the position and speed of objects moving in a circular path. Radians are also used in navigation, astronomy, and other sciences to measure angles and distances.

5. How can I convert between radians and other units of angular measurement?

In addition to converting between radians and degrees, you can also convert radians to other units such as minutes and seconds, or revolutions. To convert from radians to minutes or seconds, multiply the radian measure by 60 or 3600, respectively. To convert from radians to revolutions, divide the radian measure by 2π.

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