Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential skill for advanced math learners to understand.
First, we need to explain what radians are thereby you can see how this theorem is used in practice. Then we’ll take a further step by exhibiting some examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which implies nostril or ray, and is a fundamental theory in mathematics and geometry.
A radian is the SI (standard international) unit for angles, even though a degree is a more frequently utilized unit in math.
That being said, radians and degrees are merely two distinct units of measure employed for measuring the same 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 center of a circle to the edge, whereas a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two ways to think about this question. The first method is to figure out about how many radians exists in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). Hence, we can state:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The second way to figure out regarding this question is to calculate how many degrees exists in a radian. We understand that there are 360 degrees in a full circle, and we also understand that there are two pi radians in a full 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 useful relying upon which you're trying to get.
How to Change Radians to Degrees?
Since we've went through what degrees and radians are, let's find out how to change them!
The Formula for Changing Radians to Degrees
Proportions are a helpful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known values to obtain your unknown values. For instance, if you are required to turn .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s double-check 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 changed one type, it will always work out with another straightforward calculation. In this scenario, afterwards converting .785 from its original form back again, following these steps created precisely what was expected -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's attempt some examples, so these ideas become easier to digest.
Now, we will transform pi/12 rad into degrees. Just the same as previously, we will plug this value into the radians slot of the formula and solve it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you normally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equals 15 degrees.
Let's try some more general conversion and transform 1.047 rad to degrees. Once again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as fitting, and you will wind up with 60 degrees! (59.988 degrees to be exact).
Right away, what to do if you want to transform degrees to radians?
By employing the very exact formula, you can do the contrary in a pinch by work out with 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 recollect the formula to solve for radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just handful of examples of how to convert radians to degrees and the other way around. Bear in mind the formula and try solving for yourself the next time you have to make a transformation between radians and degrees.
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