Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for higher arithmetic students to comprehend.
First, we are required to explain what radians are in order that you can perceive how this formula is used in practice. Thereafter we’ll take this a step further by exhibiting a few examples of going from radians to degrees easily !
What Is a Radian?
Radians are measurement units for angles. It comes from the Latin word "radix," which implies nostril or ray, and is a critical concept in mathematics and geometry.
A radian is the SI (standard international) unit for angles, although a degree is a more commonly utilized unit in math.
In other words, radians and degrees are simply 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 entirely different concepts. A radius is the distance from the middle of a circle to the border, whereas a radian is a unit of measure for angles.
Association Between Radian and Degrees
We have two manners to think about this question. The first method is to contemplate about how many radians exists 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 easily:
π radians = 180 degrees
The second way to think about this question is to consider how many degrees exists in a radian. We know that there are 360 degrees in a complete 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 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 depending upon which you're trying to do.
How to Go From Radians to Degrees?
Since we've gone through what radians and degrees are, let's find out how to change them!
The Formula for Converting Radians to Degrees
Proportions are a useful tool for changing a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply put in your given values to derive your unknown values. For instance, if you wanted to change .7854 radians into degrees, your proportion will 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 implied both ways. Let’s verify our operation by converting 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.
Once we've changed one type, it will always work with another simple calculation. In this case, after changing .785 from its first form back again, after these steps made precisely what was predicted -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 simpler to digest.
At the moment, we will change pi/12 rad to degrees. Just like before, we will plug this value into the radians slot of the formula and calculate 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 equals 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. Once again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as suitable, and you will end 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 same formula, you can do the contrary in a pinch by work out with radians as the unknown.
For example, if you wish to change 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 equation to solve for radians, you will get identical answer:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just handful of examples of how to change radians to degrees and the other way around. Remember the formula and see for yourself the next time you have to make a change between radians and degrees.
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