Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important skill for progressive arithmetic students to understand.
Initially, we need to define what radians are so that you can see how this theorem works in practice. After that we’ll take it one step further by exhibiting a few examples of going from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It comes from the Latin word "radix," which means ray or nostril, and is a fundamental idea in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, even though a degree is a more generally used unit in math.
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 confused with a radius. They are two absolety distinct things. A radius is the length from the middle of a circle to the edge, while a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
We have two ways to go about regarding this question. The first way is to think about how many radians there are in a full circle. A full circle is equals to 360 degrees or two pi radians (exactly). Therefore, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to figure out about this question is to calculate how many degrees are present in a radian. We know that there are 360 degrees in a full circle, and we also know 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 helpful relying upon which you're trying to get.
How to Convert Radians to Degrees?
Since we've went through what degrees and radians are, let's learn how to convert them!
The Formula for Changing Radians to Degrees
Proportions are a helpful tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Just put in your given values to get your unknown values. For instance, if you wished to convert .7854 radians to degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To find out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s recheck our workings by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Now that we've transformed one type, it will always work with different simple calculation. In this scenario, after changing .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 Converting Radians to Degrees
Let's attempt a few examples, so these ideas become easier to digest.
Now, we will change pi/12 rad to degrees. Just the same as previously, we will plug this number in the radians slot of the formula and solve 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 result! pi/12 radians equals 15 degrees.
Let's try another general 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).
Right away, what happens if you are required to convert degrees to radians?
By employing the very exact formula, you can do the opposite in a pinch by work out with radians as the unknown.
For example, if you wish 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 remember the formula to solve for 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. Keep in mind the equation and try it out for yourself the next time you are required to make a conversion among radians and degrees.
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