Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for progressive arithmetic students to comprehend.
First, we need to specify what radians are thereby you can understand how this formula is used in practice. After that we’ll take a further step by showing some examples of going from radians to degrees easily !
What Is a Radian?
Radians are units of measurement for angles. It is derived from the Latin word "radix," which suggests nostril or ray, and is a fundamental idea in geometry and mathematics.
A radian is the SI (standard international) unit for angles, while a degree is a more commonly used unit in math.
Simply put, radians and degrees are merely two distinct units of measure utilized for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two completely separate concepts. A radius is the distance from the center of a circle to the edge, while a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
We have two manners to think regarding this question. The initial way is to think about how many radians exists in a full circle. A full circle is equal to 360 degrees or two pi radians (precisely). So, we can state:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to figure out regarding this question is to think about how many degrees exists in a radian. We know that there are 360 degrees in a whole circle, and we also recognize that there are two pi radians in a whole circle.
If we divide each side by π radians, we’ll notice that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial relying upon which you're trying to do.
How to Go From Radians to Degrees?
Now that we've gone through what degrees and radians are, let's learn how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Simply put in your known values to obtain your unknown values. For instance, if you wished to turn .7854 radians to degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To solve for z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s recheck our work by reverting 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.
Once we've changed one type, it will always work with different straightforward calculation. In this case, afterwards converting .785 from its original form back again, following these steps made exactly 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 try a handful of examples, so these ideas become simpler to digest.
Now, we will change pi/12 rad to degrees. Just like previously, we will put this number in the radians slot of the formula and work it out 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 the answer! pi/12 radians equals 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as appropriate, and you will find yourself with 60 degrees! (59.988 degrees to be almost exact).
Now, what happens if you want to convert 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 have to transform 60 degrees to radians, put in the knowns and solve for the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you remember the equation to find radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to convert radians to degrees and the other way around. Bear in mind the formula and try it out for yourself the next time you have to make a change among radians and degrees.
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