Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential skill for advanced arithmetic learners to comprehend.
Initially, we are required to specify what radians are in order that you can see how this theorem is used in practice. Then we’ll take a further step by showing some examples of going from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which implies ray or nostril, and is a essential concept in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more frequently used unit in math.
Simply put, radians and degrees are simply 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 absolety different things. A radius is the length from the center of a circle to the edge, though a radian is a measuring unit for angles.
Association Between Radian and Degrees
There are two manners to think regarding this question. The first method is to figure out about how many radians exists in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). So, we can say:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The second way to think regarding this question is to consider how many degrees are present in a radian. We know that there are 360 degrees in a full circle, and we also understand that there are two pi radians in a whole circle.
If we divide each side by π radians, we’ll notice that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are useful depending upon which you're trying to get.
How to Go From Radians to Degrees?
Since we've covered what radians and degrees are, let's practice how to convert 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
Just plug in your given values to obtain your unknown values. For instance, if you wished to turn .7854 radians into degrees, your proportion would 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 works both ways. Let’s double-check our operation by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Once we've changed one type, it will always work with another straightforward calculation. In this case, after converting .785 from its original form back again, following these steps made perfectly what was anticipated -45°.
The formulas plays out 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 theorems become simpler to digest.
Now, we will convert pi/12 rad into degrees. Much like previously, we will place 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 do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equals 15 degrees.
Let's try another general conversion and transform 1.047 rad to degrees. Yet again, 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 to do if you are required to change 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 have to transform 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 find radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just some of the examples of how to convert radians to degrees and vice versa. Remember the equation and see for yourself the next time you have to make a conversion from or to radians and degrees.
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