Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important skill for higher math students to grasp.
First, we need to explain what radians are thereby you can see how this formula works in practice. Then we’ll take a further step by exhibiting some examples of changing 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 suggests nostril or ray, and is a critical concept in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, while a degree is a more commonly used unit in mathematics.
That being said, radians and degrees are merely two distinct units of measure used for measuring the exact thing: angles.
Note: a radian is not to be mixed with a radius. They are two absolety different concepts. A radius is the length from the center of a circle to the edge, while a radian is a unit of measure for angles.
Association Between Radian and Degrees
We have two manners to think about this question. The initial 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 (precisely). Therefore, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to think regarding this question is to think about how many degrees exists in a radian. We know that there are 360 degrees in a full circle, and we also know that there are two pi radians in a full 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 relying on what you're trying to get.
How to Go From Radians to Degrees?
Now that we've went through what degrees and radians are, let's practice how to convert them!
The Formula for Changing Radians to Degrees
Proportions are a helpful tool for changing 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 wished to convert .7854 radians into degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To solve for z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s recheck 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.
Once we've converted one type, it will always work out with another unsophisticated calculation. In this scenario, afterwards changing .785 from its original form back again, after these steps made 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 attempt a handful of examples, so these ideas become easier to digest.
Now, we will convert pi/12 rad into degrees. Just like before, we will plug 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 usually would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equivalents 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as fitting, and you will wind up with 60 degrees! (59.988 degrees to be exact).
Right away, what to do if you are required to change degrees to radians?
By utilizing the very same formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you have to convert 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 recollect the formula to solve for radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just handful of examples of how to change radians to degrees and conversely. Bear in mind the equation and try solving for yourself the next time you have to make a conversion between radians and degrees.
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