Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for progressive math students to understand.
First, we are required to define what radians are in order that you can understand how this theorem works in practice. Then we’ll take it one step further by exhibiting a few examples of converting from radians to degrees with ease!
What Is a Radian?
Radians are measurement units for angles. It comes from the Latin word "radix," which implies ray or nostril, and is a critical concept in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, although a degree is a more generally used unit in math.
In other words, radians and degrees are just two separate units of measure utilized for measuring the same thing: angles.
Note: a radian is not to be mixed with a radius. They are two entirely separate concepts. A radius is the distance from the center of a circle to the edge, whereas a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
There are two ways to go about regarding this question. The first method is to contemplate about how many radians there are in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). So, we can say:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to think about this question is to think about 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 complete circle.
If we divide each side by π radians, we’ll get that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial relying on what you're trying to get.
How to Convert Radians to Degrees?
Since we've went through what degrees and radians are, let's learn how to turn them!
The Formula for Giong From Radians to Degrees
Proportions are a useful tool for changing a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Just put in your known values to get your unknown values. For example, if you wished to turn .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 can be implemented both ways. Let’s verify our work 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.
Now that we've converted one type, it will always work with different simple calculation. In this scenario, after converting .785 from its first form back again, ensuing these steps made exactly what was expected -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's try a few examples, so these concepts become easier to digest.
At the moment, we will convert pi/12 rad to degrees. Just the same as previously, we will put this value in the radians slot of the formula and calculate it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you generally would:
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
Once again, you multiply and divide as suitable, and you will find yourself with 60 degrees! (59.988 degrees to be almost exact).
Right away, what to do if you have to change degrees to radians?
By employing the very same formula, you can do the opposite in a pinch by solving it considering radians as the unknown.
For example, if you wish to convert 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 solve for radians, you will get the same thing:
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 vice versa. Keep in mind the equation and see for yourself the next time you are required to make a conversion among radians and degrees.
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