Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important skill for progressive math learners to comprehend.
Initially, we need to specify what radians are so that you can perceive how this theorem works in practice. Thereafter we’ll take it one step further by showing some examples of converting from radians to degrees easily !
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which implies ray or nostril, and is a fundamental theory in geometry and mathematics.
A radian is the SI (standard international) unit for angles, while a degree is a more generally utilized unit in mathematics.
That being said, radians and degrees are simply two different units of measure utilized for measuring the identical thing: angles.
Note: a radian is not to be mistaken with a radius. They are two completely different concepts. A radius is the length from the center of a circle to the perimeter, whereas a radian is a unit of measure for angles.
Association Between Radian and Degrees
We have two ways to go about regarding this question. The first way is to contemplate about how many radians are present in a full circle. A full circle is equivalent to 360 degrees or two pi radians (exactly). Hence, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to figure out regarding this question is to consider how many degrees there are 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 complete circle.
If we divide each side by π radians, we’ll get that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are useful depending on what you're trying to do.
How to Convert Radians to Degrees?
Now that we've gone through what radians and degrees are, let's learn how to turn them!
The Formula for Converting Radians to Degrees
Proportions are a helpful tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply plug in your known values to derive your unknown values. For example, if you are required to turn .7854 radians to degrees, your proportion would 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 can be implemented both ways. Let’s verify our operation by converting 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.
Since we've converted one type, it will always work with different unsophisticated calculation. In this case, afterwards converting .785 from its original form back again, following these steps created precisely what was predicted -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's go through a handful of examples, so these concepts become simpler to digest.
At the moment, we will convert pi/12 rad to degrees. Just like previously, we will put this number in 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 would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. One more time, utilize the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as suitable, and you will end up with 60 degrees! (59.988 degrees to be exact).
Right away, what to do if you want to convert degrees to radians?
By utilizing the very same formula, you can do the converse in a pinch by solving for radians as the unknown.
For example, if you wish to convert 60 degrees to radians, plug in the knowns and solve for the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you recollect the equation to find radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to convert radians to degrees and conversely. Bear in mind the formula and try solving for yourself the next time you are required to make a change among radians and degrees.
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