Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for advanced arithmetic learners to understand.
Initially, we are required to define what radians are in order that you can see how this formula works in practice. After that we’ll take a further step by showing some examples of changing from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It comes from the Latin word "radix," which suggests nostril or ray, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) unit for angles, although a degree is a more commonly utilized unit in arithmetic.
In other words, radians and degrees are just two distinct units of measure employed for measuring the identical thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely different things. A radius is the length from the middle of a circle to the edge, whereas a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
There are two manners to think regarding 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 (precisely). Therefore, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to think about this question is to calculate how many degrees there are in a radian. We know that there are 360 degrees in a whole circle, and we also understand that there are two pi radians in a whole 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 upon which you're trying to do.
How to Go From Radians to Degrees?
Since we've covered what degrees and radians are, let's find out how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a helpful tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply plug in your given values to obtain your unknown values. For example, if you wanted to turn .7854 radians to 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 implied both ways. Let’s recheck our operation 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 with different simple calculation. In this instance, afterwards changing .785 from its first form back again, after these steps produced precisely what was expected -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's go through some examples, so these ideas become simpler to digest.
At the moment, we will change pi/12 rad into degrees. Just like previously, 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 normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equals 15 degrees.
Let's try one more general 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 appropriate, and you will end up with 60 degrees! (59.988 degrees to be almost exact).
Now, what happens if you want to transform degrees to radians?
By utilizing the very exact formula, you can do the contrary in a pinch by solving for radians as the unknown.
For example, if you want to convert 60 degrees to radians, plug 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 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 some of the examples of how to convert radians to degrees and conversely. Keep in mind the formula and see for yourself the next time you need to make a change among radians and degrees.
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