Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for higher math learners to understand.
First, we are required to specify what radians are thereby you can see how this theorem works in practice. Thereafter we’ll take this a step further by looking at 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 means ray or nostril, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, although a degree is a more generally utilized unit in mathematics.
In other words, radians and degrees are just two different units of measure employed for measuring the exact thing: angles.
Note: a radian is not to be mixed with a radius. They are two entirely different things. A radius is the length from the center of a circle to the edge, whereas a radian is a measuring unit for angles.
Association Between Radian and Degrees
There are two ways to think regarding 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 (exactly). Therefore, we can state:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The next way to think about this question is to think about how many degrees exists 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 whole circle.
If we divide each side by π radians, we’ll see 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 get.
How to Change Radians to Degrees?
Since we've went through what radians and degrees are, let's practice how to change them!
The Formula for Giong From 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 given values to obtain your unknown values. For example, if you wanted to convert .7854 radians to degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s double-check our operation by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Since we've converted one type, it will always work with different unsophisticated calculation. In this case, afterwards changing .785 from its original form back again, following these steps produced precisely what was expected -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's go through a handful of examples, so these concepts become simpler to digest.
At the moment, we will change pi/12 rad into degrees. Much like before, we will plug this number in the radians slot of the formula and calculate it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you normally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equals 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
One more time, you multiply and divide as fitting, and you will wind up with 60 degrees! (59.988 degrees to be exact).
Right away, what happens if you are required to transform degrees to radians?
By utilizing the very same formula, you can do the opposite in a pinch by solving it considering 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 memorized the formula to find radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just some of the examples of how to convert radians to degrees and vice versa. Keep in mind the equation and see for yourself the next time you are required to make a transformation between radians and degrees.
Improve Your Skills Today with Grade Potential
When we consider mathematics, there's nothing as such as a stupid question. If you find it difficult to comprehend a concept, the best thing can be done is ask for help.
This is where Grade Potential walks in. Our expert teachers are here to assist you with all kinds of mathematics problem, whether straightforward or complicated. We'll work with you at your own convenience to make sure that you actually understand the subject.
Preparing for a examination? We will assist you produce a individualized study timetable and give you tips on how to reduce examination anxiety. So do not be worried to ask for guidance - we're here to assure you thrive.
