Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for higher mathematics students to understand.
First, we need to explain what radians are in order that you can see how this theorem is used in practice. After that we’ll take this a step further by exhibiting 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 means ray or nostril, and is a fundamental idea in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, even though a degree is a more generally used unit in arithmetic.
Simply put, radians and degrees are just two distinct units of measure used for measuring the identical thing: angles.
Note: a radian is not to be mixed with a radius. They are two entirely different concepts. A radius is the length from the center of a circle to the border, whereas a radian is a measuring unit for angles.
Association Between Radian and Degrees
There are two ways to go about about this question. The first way is to think about how many radians exists in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). Hence, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to think regarding this question is to think about how many degrees are present in a radian. We all know that there are 360 degrees in a whole 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 helpful depending on what you're trying to do.
How to Change Radians to Degrees?
Since we've went through what degrees and radians are, let's find out how to change them!
The Formula for Converting Radians to Degrees
Proportions are a helpful tool for turning a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just put in your known values to get your unknown values. For instance, if you wished 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 works both ways. Let’s recheck our workings by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Once we've changed one type, it will always work with different simple calculation. In this scenario, afterwards changing .785 from its first form back again, after these steps created exactly what was predicted -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's attempt a handful of examples, so these ideas become easier to digest.
Now, we will convert pi/12 rad into degrees. Just the same as before, we will place 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 usually would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equivalents 15 degrees.
Let's try another common conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as suitable, and you will wind up with 60 degrees! (59.988 degrees to be almost exact).
Now, what happens if you have to change degrees to radians?
By utilizing 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 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 remember 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 transform radians to degrees and the other way around. Remember the formula and try it out for yourself the next time you have to make a conversion from or to radians and degrees.
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