Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for advanced arithmetic students to grasp.
Initially, we need to specify what radians are thereby you can perceive how this formula works in practice. After that we’ll take this a step further by exhibiting some examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which means nostril or ray, and is a fundamental idea in geometry and mathematics.
A radian is the SI (standard international) unit for angles, even though a degree is a more commonly used unit in arithmetic.
Simply put, radians and degrees are merely 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 separate concepts. A radius is the length from the middle of a circle to the perimeter, while a radian is a measuring unit for angles.
Relationship Between Radian and Degrees
We have two ways to think about this question. The initial way is to figure out about how many radians there are in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). So, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to figure out regarding this question is to calculate how many degrees there are in a radian. We know that there are 360 degrees in a whole circle, and we also understand 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 useful relying on what you're trying to get.
How to Convert Radians to Degrees?
Since we've covered what radians and degrees are, let's learn how to change them!
The Formula for Giong From Radians to Degrees
Proportions are a beneficial tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to derive your unknown values. For example, if you wanted 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 can be implemented both ways. Let’s verify our operation by converting 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.
Since we've converted one type, it will always work with different simple calculation. In this instance, after changing .785 from its first form back again, ensuing these steps created perfectly what was anticipated -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's try a few examples, so these theorems become simpler to digest.
At the moment, we will transform pi/12 rad to degrees. Much like before, we will put this number 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 normally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equals 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be precise).
Now, what happens if you have to convert degrees to radians?
By using the very same formula, you can do the opposite in a pinch by work out with radians as the unknown.
For example, if you want to convert 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 memorized the formula 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 handful of examples of how to change radians to degrees and conversely. Bear in mind the equation and try solving for yourself the next time you are required to make a change among radians and degrees.
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