Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for progressive math learners to comprehend.
Initially, we are required to define what radians are so that you can perceive how this theorem works in practice. After that we’ll take a further step by looking at a few examples of converting from radians to degrees with ease!
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which suggests ray or nostril, and is a critical theory in mathematics and geometry.
A radian is the SI (standard international) unit for angles, although a degree is a more frequently used unit in math.
Simply put, radians and degrees are just two distinct units of measure employed for measuring the exact thing: angles.
Note: a radian is not to be mixed with a radius. They are two entirely separate concepts. A radius is the distance from the middle of a circle to the edge, while a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two ways to go about about this question. The first method is to figure out about how many radians there are in a full circle. A full circle is equals to 360 degrees or two pi radians (exactly). Hence, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to figure out regarding this question is to consider how many degrees exists in a radian. We all know that there are 360 degrees in a full circle, and we also recognize 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 beneficial depending on what you're trying to get.
How to Go From Radians to Degrees?
Since we've went through what degrees and radians are, let's learn how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a useful tool for turning a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your given values to derive 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 find out the value of z, multiply 180 by .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 work out the value of 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 straightforward calculation. In this instance, after changing .785 from its first form back again, following these steps produced perfectly what was anticipated -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 some examples, so these concepts become easier to digest.
Now, we will change pi/12 rad to degrees. Just like before, we will place this value in the radians slot of the formula and solve it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you usually do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equals 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. Once again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as appropriate, and you will wind up with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you want to convert degrees to radians?
By employing the very same formula, you can do the converse in a pinch by solving it considering radians as the unknown.
For example, if you want to change 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 remember the equation to solve for radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there you have it! These are just a few examples of how to transform radians to degrees and vice versa. Keep in mind the equation and try it out for yourself the next time you have to make a conversion from or to radians and degrees.
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