Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for higher math students to comprehend.
Initially, we need to specify what radians are in order that you can perceive how this formula 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 derived from the Latin word "radix," which means nostril or ray, and is a essential concept in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more frequently used unit in mathematics.
Simply put, radians and degrees are merely two distinct units of measure used for measuring the exact thing: angles.
Note: a radian is not to be mistaken with a radius. They are two absolety distinct concepts. A radius is the length from the center of a circle to the perimeter, while a radian is a unit of measure for angles.
Correlation Between Radian and Degrees
We have two manners to think about this question. The first method is to contemplate about how many radians there are in a full circle. A full circle is equal to 360 degrees or two pi radians (precisely). So, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to think about this question is to think about how many degrees are present in a radian. We understand that there are 360 degrees in a complete circle, and we also know that there are two pi radians in a complete 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 depending upon which you're trying to do.
How to Convert Radians to Degrees?
Now that we've went through what radians and degrees are, let's learn how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a beneficial tool for turning a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your known values to obtain your unknown values. For instance, if you are required to convert .7854 radians to degrees, your proportion will 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 implied both ways. Let’s double-check our work by converting 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 changed one type, it will always work with different straightforward calculation. In this instance, afterwards converting .785 from its original form back again, following these steps made 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 try a handful of examples, so these theorems become easier to digest.
Now, we will transform pi/12 rad into degrees. Just like before, we will place this number into 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 normally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equals 15 degrees.
Let's try another general conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, 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 have to convert degrees to radians?
By employing the very same formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you have to transform 60 degrees to radians, put in the knowns and work out with the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you memorized the formula to solve for radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there you have it! These are just handful of examples of how to transform radians to degrees and conversely. Keep in mind the formula and see for yourself the next time you are required to make a change between radians and degrees.
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