Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential skill for progressive mathematics students to comprehend.
Initially, we are required to specify what radians are thereby you can perceive how this formula works in practice. Then we’ll take a further step by showing a few examples of converting 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 means nostril or ray, and is a critical concept in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more frequently utilized unit in mathematics.
That being said, 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 completely separate things. A radius is the length from the middle of a circle to the border, whereas a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two manners to think about this question. The initial method is to think 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 state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to think about this question is to calculate how many degrees are present in a radian. We all know that there are 360 degrees in a full 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 notice that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful depending on what you're trying to do.
How to Change Radians to Degrees?
Now that we've covered what radians and degrees are, let's find out how to turn them!
The Formula for Giong From Radians to Degrees
Proportions are a useful tool for turning a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to obtain your unknown values. For example, if you wanted to turn .7854 radians into 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 workings 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 converted one type, it will always work out with another simple calculation. In this scenario, after converting .785 from its original form back again, ensuing these steps made exactly 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 concepts become simpler to digest.
At the moment, we will convert pi/12 rad into degrees. Just like previously, we will place this number in the radians slot of the formula and calculate it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you usually would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 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
One more time, you multiply and divide as appropriate, and you will find yourself with 60 degrees! (59.988 degrees to be precise).
Right away, what happens if you are required to change degrees to radians?
By using the very same formula, you can do the opposite in a pinch by solving for radians as the unknown.
For example, if you wish to transform 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 equation to solve for radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there you have it! These are just some of the examples of how to change radians to degrees and the other way around. Remember the formula and try it out for yourself the next time you need to make a conversion from or to radians and degrees.
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