Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for advanced math learners to understand.
Initially, we need to define what radians are so that you can see how this formula is used in practice. Then we’ll take a further step by showing a few examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which implies ray or nostril, and is a fundamental theory in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more frequently used unit in math.
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 confused with a radius. They are two absolety separate concepts. A radius is the distance from the middle of a circle to the border, though a radian is a measuring unit for angles.
Relationship Between Radian and Degrees
There are two ways to think regarding this question. The first method is to contemplate about how many radians there are in a full circle. A full circle is equals to 360 degrees or two pi radians (exactly). Hence, we can state:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to think about this question is to calculate how many degrees exists 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 get that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful relying on what you're trying to do.
How to Convert Radians to Degrees?
Since we've covered what degrees and radians are, let's practice how to change them!
The Formula for Converting Radians to Degrees
Proportions are a useful tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known values to obtain your unknown values. For example, if you are required 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 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s recheck our workings by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Now that we've transformed one type, it will always work out with different unsophisticated calculation. In this scenario, afterwards converting .785 from its first form back again, following these steps created precisely what was predicted -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's try a few examples, so these ideas become simpler to digest.
At the moment, we will change pi/12 rad into degrees. Just the same as before, we will plug this number 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 usually do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 15 degrees.
Let's try one more general conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as appropriate, 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 employing the very exact formula, you can do the contrary in a pinch by work out with radians as the unknown.
For example, if you have 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 recollect the formula to find 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 a few examples of how to transform radians to degrees and conversely. Remember the formula and try it out for yourself the next time you have to make a conversion among radians and degrees.
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