Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for higher math learners to understand.
First, we need to specify what radians are so that you can perceive how this theorem works in practice. Then 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 originated from the Latin word "radix," which implies nostril or ray, and is a essential theory in mathematics and geometry.
A radian is the SI (standard international) unit for angles, although a degree is a more commonly utilized unit in arithmetic.
Simply put, radians and degrees are just two distinct units of measure utilized for measuring the identical thing: angles.
Note: a radian is not to be mixed with a radius. They are two absolety distinct concepts. A radius is the distance from the middle of a circle to the border, though a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
There are two ways to go about about this question. The first way is to contemplate about how many radians are present in a full circle. A full circle is equivalent to 360 degrees or two pi radians (exactly). Therefore, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to think regarding this question is to think about how many degrees there are in a radian. We know that there are 360 degrees in a whole circle, and we also recognize that there are two pi radians in a full 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 beneficial relying upon which you're trying to get.
How to Change Radians to Degrees?
Now that we've gone through what radians and degrees are, let's find out how to turn them!
The Formula for Giong From Radians to Degrees
Proportions are a helpful tool for turning 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 convert .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 can be implemented both ways. Let’s recheck our workings by reverting 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.
Now that we've converted one type, it will always work out with different unsophisticated calculation. In this case, afterwards converting .785 from its original form back again, ensuing these steps created perfectly what was anticipated -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's go through a few examples, so these ideas become simpler to digest.
Now, we will transform pi/12 rad to degrees. Much like 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 normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equals 15 degrees.
Let's try some more 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 suitable, and you will end up with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you want to change degrees to radians?
By using the very exact formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you have to change 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 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 the other way around. Remember the formula and try solving for yourself the next time you have to make a change between radians and degrees.
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