Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential skill for progressive arithmetic students to grasp.
Initially, we are required to specify what radians are thereby you can see how this formula works in practice. Thereafter we’ll take a further step by exhibiting a few examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which implies ray or nostril, and is a essential theory in geometry and mathematics.
A radian is the SI (standard international) unit for angles, while a degree is a more commonly used unit in math.
That being said, radians and degrees are simply 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 manners to go about about this question. The initial method is to contemplate 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 state:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The next way to think regarding this question is to consider how many degrees there are in a radian. We know that there are 360 degrees in a complete circle, and we also recognize that there are two pi radians in a whole 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 upon which you're trying to get.
How to Go From Radians to Degrees?
Since we've went through what radians and degrees are, let's practice how to turn them!
The Formula for Giong From Radians to Degrees
Proportions are a useful tool for turning a radian value into degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your known values to obtain your unknown values. For example, if you wanted to change .7854 radians to 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 works both ways. Let’s double-check our workings by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Now that we've changed one type, it will always work out with another simple calculation. In this instance, after changing .785 from its original form back again, ensuing these steps created perfectly what was expected -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's attempt a few examples, so these theorems become easier to digest.
Now, we will transform pi/12 rad into degrees. Much like previously, we will plug this number into the radians slot of the formula and solve 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 equivalents 15 degrees.
Let's try another general conversion and transform 1.047 rad to degrees. One more time, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as fitting, and you will end up with 60 degrees! (59.988 degrees to be almost exact).
Now, what happens if you have to change degrees to radians?
By employing the very same formula, you can do the opposite in a pinch by solving for radians as the unknown.
For example, if you wish to convert 60 degrees to radians, put 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 equation to solve for 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 a few examples of how to change radians to degrees and the other way around. Keep in mind the formula and try solving for yourself the next time you have to make a conversion between radians and degrees.
Improve Your Skills Today with Grade Potential
When we consider mathematics, there's nothing as such as a foolish question. If you're struggling to understand a concept, the best thing can be done is ask for assistance.
This is where Grade Potential enters. Our experienced instructors are here to guide you with any kind of mathematics problem, whether simple or difficult ones. We'll work with you at your own pace to make sure that you truly comprehend the subject.
Preparing for a exam? We will assist you create a individualized study plan and give you tips on how to lower test anxiety. So do not be worried to inquire for help - we're here to ensure you prosper.
