Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential skill for progressive arithmetic learners to understand.
First, we need to explain what radians are so that you can see how this theorem works in practice. Thereafter we’ll take it one step further by looking at a few examples of changing from radians to degrees easily !
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 essential concept in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more generally utilized unit in mathematics.
In other words, radians and degrees are just two distinct units of measure utilized for measuring the same thing: angles.
Note: a radian is not to be mixed with a radius. They are two entirely distinct concepts. A radius is the length from the middle of a circle to the border, whereas a radian is a measuring unit for angles.
Association Between Radian and Degrees
There are two ways to think regarding this question. The first way is to think about how many radians exists in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). Hence, we can say:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The next way to figure out regarding this question is to think about how many degrees are present in a radian. We all know that there are 360 degrees in a whole circle, and we also recognize 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 beneficial depending on what you're trying to do.
How to Convert Radians to Degrees?
Now that we've went through what radians and degrees are, let's find out how to change them!
The Formula for Giong From Radians to Degrees
Proportions are a helpful tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to obtain your unknown values. For instance, if you are required to change .7854 radians into 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 can be implemented 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 by 3.14 (pi) and divide by 180: .785 radians.
Since we've converted one type, it will always work with different straightforward calculation. In this instance, after converting .785 from its original form back again, ensuing these steps produced exactly what was predicted -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 concepts become simpler to digest.
At the moment, we will change pi/12 rad into degrees. Just like previously, we will put 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 generally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equals 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
Once again, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Now, what happens if you have to change degrees to radians?
By using the very exact formula, you can do the opposite in a pinch by solving for radians as the unknown.
For example, if you wish to change 60 degrees to radians, plug in the knowns and work out with the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you remember 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 change radians to degrees and conversely. Bear in mind the equation and try solving for yourself the next time you need to make a transformation among radians and degrees.
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