Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for advanced mathematics learners to understand.
Initially, we are required to define what radians are so that you can perceive how this theorem works in practice. Thereafter we’ll take this a step further by showing a few examples of going from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a critical concept in mathematics and geometry.
A radian is the SI (standard international) unit for angles, although a degree is a more generally utilized unit in arithmetic.
Simply put, radians and degrees are just two distinct units of measure utilized for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two absolety distinct things. A radius is the distance from the center of a circle to the perimeter, though a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
There are two ways to go about regarding this question. The initial method is to figure out 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 say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to figure out about this question is to consider how many degrees exists in a radian. We all know that there are 360 degrees in a whole circle, and we also recognize 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 approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial depending on what you're trying to do.
How to Convert Radians to Degrees?
Since we've went through what radians and degrees are, let's practice how to change them!
The Formula for Converting Radians to Degrees
Proportions are a helpful tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known values to obtain your unknown values. For example, if you wished to turn .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 can be implemented both ways. Let’s recheck our work by reverting 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.
Since we've changed one type, it will always work with another unsophisticated calculation. In this instance, afterwards changing .785 from its first form back again, following these steps made exactly what was predicted -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's try a handful of examples, so these concepts become easier to digest.
Now, we will transform 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 normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as appropriate, and you will end up with 60 degrees! (59.988 degrees to be precise).
Now, what happens if you have to convert degrees to radians?
By using 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, put in the knowns and solve for the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you remember the formula to find radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just handful of examples of how to convert radians to degrees and conversely. Keep in mind the formula and try solving for yourself the next time you need to make a conversion between radians and degrees.
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