Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important skill for progressive math students to comprehend.
Initially, we need to define what radians are thereby you can perceive how this theorem works in practice. Thereafter we’ll take it one step further by exhibiting some examples of converting 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 implies ray or nostril, and is a critical concept in geometry and mathematics.
A radian is the SI (standard international) unit for angles, although a degree is a more commonly utilized unit in arithmetic.
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 mistaken with a radius. They are two completely different things. A radius is the length from the center of a circle to the edge, while a radian is a unit of measure for angles.
Correlation Between Radian and Degrees
There are two manners to think about this question. The initial method is to contemplate 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 consider how many degrees there are in a radian. We all know that there are 360 degrees in a full 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 beneficial depending upon which you're trying to get.
How to Go From Radians to Degrees?
Now that we've covered what degrees and radians are, let's practice how to convert them!
The Formula for Giong From Radians to Degrees
Proportions are a useful tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
With ease put in your known values to derive your unknown values. For instance, if you wanted to convert .7854 radians into degrees, your proportion would 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 implied both ways. Let’s recheck our workings by converting 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 converted one type, it will always work with different simple calculation. In this scenario, afterwards converting .785 from its first form back again, following these steps created perfectly what was predicted -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 attempt some examples, so these ideas become easier to digest.
At the moment, we will transform pi/12 rad into degrees. Just like before, we will put 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 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. Yet again, 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).
Right away, what happens if you want to transform degrees to radians?
By employing the very same formula, you can do the converse in a pinch by work out with radians as the unknown.
For example, if you want 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 equation 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 transform radians to degrees and conversely. Keep in mind the equation and try it out for yourself the next time you need to make a change among radians and degrees.
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