Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for progressive arithmetic learners to grasp.
Initially, we need to specify what radians are so that you can understand how this theorem is used in practice. Thereafter we’ll take a further step by showing a few examples of going from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which suggests ray or nostril, and is a fundamental concept in geometry and mathematics.
A radian is the SI (standard international) unit for angles, even though a degree is a more frequently used unit in mathematics.
In other words, radians and degrees are just two different units of measure employed for measuring the same thing: angles.
Note: a radian is not to be mistaken with a radius. They are two entirely different things. A radius is the length from the center of a circle to the border, though a radian is a unit of measure for angles.
Association Between Radian and Degrees
There are two manners to think about this question. The first way is to figure out about how many radians are present in a full circle. A full circle is equivalent to 360 degrees or two pi radians (exactly). So, we can say:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The second way to figure out regarding this question is to calculate how many degrees are present in a radian. We know that there are 360 degrees in a whole circle, and we also know 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 about 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 do.
How to Convert Radians to Degrees?
Since we've went through what degrees and radians are, let's learn how to turn 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
Simply put in your known values to get your unknown values. For example, if you wanted to convert .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 implied both ways. Let’s double-check 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 another simple calculation. In this case, afterwards changing .785 from its first form back again, following these steps made 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. Just the same as before, we will place this number in 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 do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equivalents 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as fitting, and you will end up with 60 degrees! (59.988 degrees to be almost exact).
Right away, what happens if you are required to transform degrees to radians?
By employing the very same formula, you can do the converse in a pinch by solving for radians as the unknown.
For example, if you wish 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 remember the equation to solve for radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to convert radians to degrees and the other way around. Remember the formula and see for yourself the next time you have to make a transformation between radians and degrees.
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