Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for progressive math learners to comprehend.
Initially, we need to specify what radians are so that you can perceive how this formula works in practice. Thereafter we’ll take this a step further by exhibiting some examples of going from radians to degrees with ease!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which suggests nostril or ray, and is a critical idea in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more generally used unit in math.
Simply put, radians and degrees are merely two different units of measure used for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely different things. A radius is the distance from the middle of a circle to the perimeter, whereas a radian is a measuring unit for angles.
Relationship Between Radian and Degrees
There are two manners to go about about this question. The first way is to contemplate 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 state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to figure out about this question is to consider how many degrees are present in a radian. We know that there are 360 degrees in a complete circle, and we also recognize that there are two pi radians in a whole circle.
If we divide each side by π radians, we’ll get 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?
Now that we've went through what degrees and radians are, let's find out how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a beneficial tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just put in your given values to derive your unknown values. For example, if you are required to turn .7854 radians to degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s recheck our operation by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find 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 straightforward calculation. In this case, after converting .785 from its original form back again, ensuing these steps created perfectly 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 attempt a handful of examples, so these ideas become easier to digest.
Now, we will change pi/12 rad to degrees. Just the same as before, we will put this value into the radians slot of the formula and work it out 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 equivalents 15 degrees.
Let's try another general conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as suitable, and you will end up with 60 degrees! (59.988 degrees to be almost exact).
Right away, what happens if you are required to convert degrees to radians?
By utilizing the very same formula, you can do the opposite in a pinch by solving it considering radians as the unknown.
For example, if you want to change 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 remember the formula 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 handful of examples of how to convert radians to degrees and conversely. Bear in mind the formula and see for yourself the next time you need to make a transformation between radians and degrees.
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