Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for advanced arithmetic students to comprehend.
First, we need to specify what radians are in order that you can see how this theorem works in practice. Then we’ll take a further step by exhibiting some examples of going from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which means ray or nostril, and is a fundamental concept in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more generally utilized unit in math.
That being said, radians and degrees are just two distinct units of measure used for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely separate concepts. A radius is the distance from the center of a circle to the border, while a radian is a measuring unit for angles.
Association Between Radian and Degrees
There are two ways to think about this question. The first method is to figure out about how many radians are present in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). Therefore, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to figure out about this question is to consider how many degrees exists in a radian. We know that there are 360 degrees in a complete circle, and we also recognize that there are two pi radians in a complete circle.
If we divide each side by π radians, we’ll get that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful depending on what you're trying to do.
How to Convert Radians to Degrees?
Now that we've covered what radians and degrees are, let's practice how to turn them!
The Formula for Converting Radians to Degrees
Proportions are a useful tool for changing a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known values to get your unknown values. For instance, if you are required to change .7854 radians into degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To find out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s recheck our work by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Now that we've transformed one type, it will always work with different straightforward calculation. In this instance, after converting .785 from its first form back again, following these steps made perfectly what was anticipated -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's go through a handful of examples, so these theorems become simpler to digest.
At the moment, we will transform pi/12 rad to degrees. Just the same as previously, we will place this number in the radians slot of the formula and calculate it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you generally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equals 15 degrees.
Let's try another common conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as fitting, and you will end up with 60 degrees! (59.988 degrees to be almost exact).
Right away, what to do if you are required to transform degrees to radians?
By employing the very same formula, you can do the contrary in a pinch by solving for radians as the unknown.
For example, if you want to convert 60 degrees to radians, plug in the knowns and solve for the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you memorized the equation to solve for radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just some of the examples of how to transform radians to degrees and the other way around. Bear in mind the formula and try it out for yourself the next time you are required to make a change between radians and degrees.
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