Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for progressive math learners to grasp.
Initially, we need to define what radians are so that you can understand how this formula works in practice. Then we’ll take it one step further by exhibiting 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 implies ray or nostril, and is a fundamental idea in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more generally utilized unit in mathematics.
Simply put, radians and degrees are simply two separate units of measure employed for measuring the exact thing: angles.
Note: a radian is not to be mistaken with a radius. They are two completely different concepts. A radius is the distance from the center of a circle to the perimeter, while a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
There are two manners to go about about this question. The initial method is to contemplate 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 next way to think regarding this question is to consider how many degrees are present in a radian. We understand 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 see that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are useful depending upon which you're trying to get.
How to Change Radians to Degrees?
Since we've went through what radians and degrees are, let's learn how to change them!
The Formula for Giong From Radians to Degrees
Proportions are a beneficial tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply plug in your known values to get your unknown values. For instance, if you are required to change .7854 radians to degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s double-check our workings by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Since we've transformed one type, it will always work out with different unsophisticated calculation. In this case, afterwards converting .785 from its first form back again, following these steps produced exactly what was expected -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's attempt a handful of examples, so these ideas become simpler to digest.
At the moment, we will transform pi/12 rad into degrees. Just the same as before, we will plug this number into the radians slot of the formula and calculate it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you generally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equals 15 degrees.
Let's try another common conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
Once again, you multiply and divide as fitting, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you have to change degrees to radians?
By using the very exact formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you have to change 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 memorized the formula to find radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just some of the examples of how to convert radians to degrees and vice versa. Remember the equation and try it out for yourself the next time you need to make a change from or to radians and degrees.
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