Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for advanced arithmetic students to understand.
Initially, we are required to define what radians are so that you can see how this theorem is used in practice. Thereafter we’ll take this a step further by showing some examples of changing 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 essential idea in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, although a degree is a more generally used unit in mathematics.
That being said, radians and degrees are simply two separate units of measure used for measuring the same thing: angles.
Note: a radian is not to be mistaken with a radius. They are two completely different concepts. A radius is the distance from the middle of a circle to the border, whereas a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
There are two ways to go about about this question. The first method is to think about how many radians there are in a full circle. A full circle is equal 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 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 know 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 useful depending on what you're trying to get.
How to Convert Radians to Degrees?
Since we've went through what radians and degrees are, let's learn how to turn them!
The Formula for Giong From Radians to Degrees
Proportions are a beneficial tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
With ease put in your known values to get your unknown values. For example, if you wished to convert .7854 radians into degrees, your proportion will 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 can be implemented both ways. Let’s recheck our work by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Now that we've changed one type, it will always work out with another unsophisticated calculation. In this scenario, after converting .785 from its first form back again, ensuing these steps created exactly 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 go through a handful of examples, so these concepts become easier to digest.
At the moment, we will convert pi/12 rad to degrees. Much like before, we will put this value into the radians slot of the formula and calculate 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 answer! 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
Once again, you multiply and divide as fitting, and you will end up with 60 degrees! (59.988 degrees to be exact).
Now, what happens if you have to convert degrees to radians?
By using the very same formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you wish to transform 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 memorized the formula 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 handful of examples of how to change radians to degrees and the other way around. Keep in mind the formula and see for yourself the next time you are required to make a conversion among radians and degrees.
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