Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important skill for advanced math students to comprehend.
Initially, we are required to define what radians are thereby you can understand how this formula is used in practice. Then we’ll take this a step further by exhibiting some examples of going from radians to degrees quickly!
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which suggests ray or nostril, and is a essential concept in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more generally utilized unit in mathematics.
In other words, radians and degrees are just two distinct units of measure employed for measuring the same thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely distinct things. A radius is the distance from the middle of a circle to the border, though a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
There are two manners to think regarding this question. The initial way is to contemplate about how many radians there are in a full circle. A full circle is equivalent to 360 degrees or two pi radians (exactly). Therefore, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to think regarding this question is to consider how many degrees there are in a radian. We all know that there are 360 degrees in a complete circle, and we also understand that there are two pi radians in a full 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 upon which you're trying to get.
How to Convert Radians to Degrees?
Since we've gone 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 plug in your known values to derive your unknown values. For example, 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 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s double-check our work by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Since we've transformed one type, it will always work with another unsophisticated calculation. In this scenario, after changing .785 from its first 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 try a handful of examples, so these theorems become simpler to digest.
Now, we will change pi/12 rad into degrees. Just like previously, 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 generally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equals 15 degrees.
Let's try one more 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 appropriate, and you will end up with 60 degrees! (59.988 degrees to be precise).
Now, what happens if you are required to transform degrees to radians?
By employing the very same formula, you can do the contrary in a pinch by solving for radians as the unknown.
For example, if you have to change 60 degrees to radians, plug in the knowns and work out with the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you remember the equation to find radians, you will get the exact result:
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 vice versa. Bear in mind the equation and see for yourself the next time you are required to make a conversion among radians and degrees.
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