Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for higher mathematics students to comprehend.
First, we need to specify what radians are so that you can perceive how this formula works in practice. Then we’ll take a further step by looking at a few examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are units of measurement for angles. It is derived from the Latin word "radix," which means ray or nostril, and is a critical concept in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, while a degree is a more generally used unit in arithmetic.
In other words, radians and degrees are merely two separate units of measure utilized for measuring the same thing: angles.
Note: a radian is not to be mixed with a radius. They are two completely distinct concepts. A radius is the distance from the middle of a circle to the edge, though a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
We have two manners to go about regarding this question. The initial method is to figure out about how many radians there are in a full circle. A full circle is equal to 360 degrees or two pi radians (precisely). Therefore, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to figure out 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 complete circle.
If we divide each side by π radians, we’ll see 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 on what you're trying to do.
How to Change Radians to Degrees?
Now that we've covered what radians and degrees are, let's practice how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a helpful tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
With ease put in your known values to get your unknown values. For instance, if you are required to turn .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 can be implemented both ways. Let’s double-check our workings by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Since we've changed one type, it will always work out with another simple calculation. In this instance, after converting .785 from its original form back again, after these steps produced precisely what was predicted -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's try a handful of examples, so these ideas become simpler to digest.
At the moment, we will convert pi/12 rad to degrees. Just the same as previously, we will put this number into the radians slot of the formula and calculate 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 the result! pi/12 radians equivalents 15 degrees.
Let's try another general 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 fitting, and you will end up with 60 degrees! (59.988 degrees to be precise).
Now, what to do if you are required 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 have to change 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 solve for radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there you have it! These are just some of the examples of how to change radians to degrees and vice versa. Keep in mind the formula and try solving for yourself the next time you need to make a conversion between radians and degrees.
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