Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for progressive arithmetic students to understand.
Initially, we are required to specify what radians are so that you can see how this formula is used in practice. Then we’ll take this a step further by showing some examples of converting 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 fundamental theory in geometry and mathematics.
A radian is the SI (standard international) unit for angles, even though a degree is a more commonly used unit in arithmetic.
Simply put, radians and degrees are just two different units of measure employed for measuring the identical thing: angles.
Note: a radian is not to be mixed with a radius. They are two completely distinct things. A radius is the distance from the middle of a circle to the border, while a radian is a unit of measure for angles.
Association Between Radian and Degrees
There are two ways to go about regarding this question. The initial way is to contemplate 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 say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to think about this question is to consider how many degrees are present in a radian. We know 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 notice that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful relying on what you're trying to get.
How to Convert Radians to Degrees?
Since we've went through what radians and degrees are, let's find out 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
With ease put in your given values to obtain your unknown values. For instance, if you wished to change .7854 radians into degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To find out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s recheck our operation by converting 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 out with different straightforward calculation. In this instance, after changing .785 from its first form back again, after these steps produced exactly 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 try some examples, so these ideas become easier to digest.
At the moment, we will convert pi/12 rad to degrees. Much like before, we will plug this value into 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 it! pi/12 radians equals 15 degrees.
Let's try another common conversion and transform 1.047 rad to degrees. One more time, utilize 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 precise).
Now, what to do if you are required to transform degrees to radians?
By utilizing the very exact formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you wish to transform 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 recollect 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 vice versa. Keep in mind the formula and see for yourself the next time you need to make a conversion between radians and degrees.
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