Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for higher math learners to understand.
Initially, we need to explain what radians are so that you can see how this theorem works in practice. Thereafter we’ll take a further step by showing a few examples of going from radians to degrees easily !
What Is a Radian?
Radians are units of measurement for angles. It is derived from the Latin word "radix," which means ray or nostril, and is a critical concept in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more commonly utilized unit in math.
In other words, radians and degrees are just two different units of measure utilized for measuring the identical thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely distinct concepts. A radius is the length from the middle of a circle to the edge, though a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two ways to go about about this question. The first method is to figure out about how many radians are present 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 easily:
π radians = 180 degrees
The second way to figure out regarding this question is to consider how many degrees there are in a radian. We understand that there are 360 degrees in a complete 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 notice 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 on what you're trying to do.
How to Change Radians to Degrees?
Now that we've gone through what degrees and radians are, let's find out how to turn them!
The Formula for Giong From Radians to Degrees
Proportions are a helpful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to obtain your unknown values. For instance, if you wished to change .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To find 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 work by converting 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 changed one type, it will always work with another unsophisticated calculation. In this scenario, afterwards converting .785 from its first form back again, following 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 Converting Radians to Degrees
Let's attempt some examples, so these concepts become easier to digest.
At the moment, we will transform pi/12 rad to degrees. Just the same as previously, 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 generally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! 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
Once again, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you are required to transform degrees to radians?
By employing the very exact formula, you can do the contrary in a pinch by solving for 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 memorized the equation to solve for radians, you will get identical answer:
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 conversely. Keep in mind the equation and try it out for yourself the next time you need to make a conversion among radians and degrees.
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