Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for advanced mathematics learners to grasp.
First, we need to explain what radians are in order that you can perceive how this theorem is used in practice. After that we’ll take a further step by looking at some examples of converting from radians to degrees with ease!
What Is a Radian?
Radians are units of measurement for angles. It comes from the Latin word "radix," which suggests ray or nostril, and is a critical idea in mathematics and geometry.
A radian is the SI (standard international) unit for angles, while a degree is a more frequently utilized unit in mathematics.
In other words, radians and degrees are just two distinct 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 different concepts. A radius is the distance from the center of a circle to the perimeter, whereas a radian is a unit of measure for angles.
Association Between Radian and Degrees
There are two ways to go about regarding this question. The first way is to think about how many radians are present in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). 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 full circle, and we also recognize that there are two pi radians in a full circle.
If we divide each side by π radians, we’ll notice that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are useful relying upon which you're trying to do.
How to Go From Radians to Degrees?
Now that we've went through what degrees and radians are, let's practice how to convert them!
The Formula for Changing Radians to Degrees
Proportions are a helpful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your known values to obtain your unknown values. For instance, if you wished to convert .7854 radians to 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 can be implemented both ways. Let’s double-check our operation by changing 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.
Now that we've converted one type, it will always work with different straightforward calculation. In this scenario, afterwards changing .785 from its first form back again, ensuing these steps produced exactly what was expected -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's try a handful of examples, so these concepts become easier to digest.
Now, we will change pi/12 rad to degrees. Much like previously, we will plug this value in the radians slot of the formula and solve it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you generally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 15 degrees.
Let's try another common conversion and transform 1.047 rad to degrees. One more time, utilize the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as suitable, and you will wind up with 60 degrees! (59.988 degrees to be exact).
Right away, what to do if you have to change degrees to radians?
By utilizing the very exact formula, you can do the converse in a pinch by solving it considering radians as the unknown.
For example, if you wish to transform 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 recollect the formula to solve for radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just some of the examples of how to change radians to degrees and vice versa. Bear in mind the equation and try solving for yourself the next time you are required to make a conversion between radians and degrees.
Improve Your Skills Today with Grade Potential
When we talk about arithmetic, there's nothing as such as a stupid question. If you find yourself in trouble understanding a topic, the finest thing could be done is request for guidance.
This is where Grade Potential comes in. Our professional instructors are here to guide you with any mathematics problem, whether simple or difficult ones. We'll work by your side at your own pace to ensure that you actually understand the subject.
Getting yourself ready for a exam? We will guide you create a customized study plan and offer you tips on how to decrease examination anxiety. So do not be afraid to request for guidance - we're here to ensure you prosper.
