Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for higher arithmetic learners to comprehend.
Initially, we need to explain what radians are in order that you can see how this formula works in practice. Thereafter we’ll take a further step by exhibiting some examples of changing from radians to degrees with ease!
What Is a Radian?
Radians are units of measurement for angles. It comes from the Latin word "radix," which implies nostril or ray, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more generally used unit in math.
In other words, radians and degrees are simply two different units of measure used for measuring the same thing: angles.
Note: a radian is not to be confused with a radius. They are two absolety separate concepts. A radius is the distance from the middle 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 think about this question. The first way is to figure out about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). Hence, we can say:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The next way to think regarding this question is to calculate how many degrees there are in a radian. We understand that there are 360 degrees in a complete circle, and we also understand that there are two pi radians in a whole 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 helpful depending upon which you're trying to get.
How to Convert Radians to Degrees?
Since we've went through what degrees and radians are, let's find out how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for turning a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your given values to get your unknown values. For example, if you wished to convert .7854 radians to degrees, your proportion would 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 recheck our work 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.
Now that we've transformed one type, it will always work out with another simple calculation. In this instance, after changing .785 from its first form back again, ensuing these steps made exactly what was expected -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's go through some examples, so these theorems become easier to digest.
At the moment, we will convert pi/12 rad into degrees. Much like before, we will plug this value in the radians slot of the formula and calculate 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 it! pi/12 radians equivalents 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
Yet again, you multiply and divide as appropriate, and you will end up with 60 degrees! (59.988 degrees to be precise).
Now, what to do if you have to convert degrees to radians?
By using the very exact formula, you can do the contrary in a pinch by solving for radians as the unknown.
For example, if you wish to convert 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 memorized the equation to solve for radians, you will get identical answer:
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. Remember the equation and see for yourself the next time you need to make a transformation between radians and degrees.
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