Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for higher mathematics learners to grasp.
First, we need to explain what radians are thereby you can perceive how this theorem works in practice. Thereafter we’ll take this a step further by showing a few examples of changing 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 implies ray or nostril, and is a essential idea in mathematics and geometry.
A radian is the SI (standard international) unit for angles, although a degree is a more frequently used unit in mathematics.
Simply put, radians and degrees are simply two different units of measure utilized for measuring the exact thing: angles.
Note: a radian is not to be mistaken with a radius. They are two completely distinct things. A radius is the distance from the center of a circle to the border, while a radian is a measuring unit 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 equals to 360 degrees or two pi radians (precisely). Hence, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to think regarding this question is to calculate how many degrees are present in a radian. We all know that there are 360 degrees in a whole circle, and we also recognize 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 relying upon which you're trying to do.
How to Change Radians to Degrees?
Since we've covered what degrees and radians are, let's find out how to convert them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for turning a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Simply put in your known values to obtain your unknown values. For instance, if you wished to turn .7854 radians to 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 implied both ways. Let’s verify our workings by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Once we've transformed one type, it will always work with another straightforward calculation. In this scenario, after converting .785 from its original form back again, ensuing these steps produced exactly what was predicted -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's go through a handful of examples, so these theorems become easier to digest.
Now, we will convert pi/12 rad to degrees. Just the same as previously, we will place 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 the result! pi/12 radians equivalents 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as fitting, and you will find yourself with 60 degrees! (59.988 degrees to be precise).
Now, what happens if you want to change degrees to radians?
By utilizing the very exact formula, you can do the converse in a pinch by solving it considering radians as the unknown.
For example, if you wish 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 recollect the equation to find radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to transform radians to degrees and the other way around. Remember the formula and try solving for yourself the next time you have to make a transformation from or to radians and degrees.
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