Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for higher math students to understand.
First, we need to define what radians are thereby you can understand how this theorem is used in practice. Thereafter we’ll take this a step further by looking at some examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It comes from the Latin word "radix," which suggests ray or nostril, and is a essential theory in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more commonly used unit in mathematics.
In other words, radians and degrees are just two different units of measure utilized for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two completely different things. A radius is the distance from the center of a circle to the perimeter, while a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two manners to think regarding this question. The first method is to think about how many radians there are in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). So, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to figure out regarding this question is to think about how many degrees there are in a radian. We know that there are 360 degrees in a whole circle, and we also know 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 approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful relying on what you're trying to do.
How to Go From Radians to Degrees?
Now that we've covered what degrees and radians are, let's learn how to convert them!
The Formula for Giong From Radians to Degrees
Proportions are a helpful tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease put in your given values to derive your unknown values. For example, if you are required to turn .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To solve for 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 work by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Now that we've transformed one type, it will always work out with another simple calculation. In this case, afterwards changing .785 from its first form back again, ensuing these steps produced perfectly what was expected -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's go through a handful of examples, so these theorems become easier to digest.
Now, we will convert pi/12 rad to degrees. Just the same as previously, we will put this value 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 do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equivalents 15 degrees.
Let's try one more general conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you want to change degrees to radians?
By employing the very same formula, you can do the converse in a pinch by solving for radians as the unknown.
For example, if you wish 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 equation to find radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there you have it! These are just a few examples of how to convert radians to degrees and vice versa. Keep in mind the formula and try solving for yourself the next time you have to make a transformation between radians and degrees.
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