Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for advanced math students to comprehend.
Initially, we need to define what radians are in order that you can perceive how this theorem is used in practice. Then we’ll take this a step further by exhibiting a few examples of going from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which implies nostril or ray, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, even though a degree is a more generally utilized unit in math.
In other words, radians and degrees are simply two different units of measure employed for measuring the same thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely different concepts. A radius is the length from the center of a circle to the border, though a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two ways to go about regarding this question. The first way is to figure out 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 simplified:
π radians = 180 degrees
The second way to think about this question is to consider how many degrees are present 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 see that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful relying upon which you're trying to get.
How to Go From Radians to Degrees?
Since we've covered what degrees and radians are, let's find out how to turn them!
The Formula for Converting Radians to Degrees
Proportions are a helpful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your given values to derive your unknown values. For example, if you wanted to change .7854 radians into degrees, your proportion will 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 double-check our operation by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Since we've transformed one type, it will always work with another unsophisticated calculation. In this instance, after converting .785 from its original form back again, following these steps created precisely what was expected -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's go through some examples, so these ideas become simpler to digest.
Now, we will convert pi/12 rad to degrees. Much like before, we will place this number in the radians slot of the formula and solve it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you usually do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 15 degrees.
Let's try some more general 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 find yourself with 60 degrees! (59.988 degrees to be precise).
Right away, what to do if you are required to change degrees to radians?
By utilizing the very same formula, you can do the opposite in a pinch by work out with radians as the unknown.
For example, if you have to change 60 degrees to radians, plug 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 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 handful of examples of how to transform radians to degrees and vice versa. Keep in mind the equation and see 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 consider arithmetic, there's nothing as such as a silly question. If you find yourself in trouble understanding a concept, the best thing you can do is request for help.
That's where Grade Potential enters. Our professional tutors are here to guide you with all kinds of mathematics problem, whether simple or difficult ones. We'll work with you at your own convenience to make sure that you really comprehend the subject.
Getting yourself ready for a examination? We will guide you create a customized study plan and provide you tips on how to decrease examination anxiety. So do not be afraid to request for help - we're here to make sure you prosper.
