Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for progressive mathematics students to understand.
First, we are required to explain what radians are in order that you can see how this theorem is used in practice. Thereafter we’ll take a further step by showing some examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, although a degree is a more commonly used unit in math.
Simply put, radians and degrees are just two separate units of measure used for measuring the same thing: angles.
Note: a radian is not to be mistaken with a radius. They are two absolety distinct things. A radius is the distance from the center of a circle to the edge, whereas a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
We have two manners to think about this question. The first method is to contemplate about how many radians are present in a full circle. A full circle is equivalent 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 consider how many degrees there are in a radian. We all know that there are 360 degrees in a full 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 notice that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are useful depending upon which you're trying to get.
How to Convert Radians to Degrees?
Now that we've covered what radians and degrees are, let's find out how to change them!
The Formula for Converting Radians to Degrees
Proportions are a beneficial tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to get your unknown values. For example, if you are required to change .7854 radians to degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To work 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 recheck our workings by reverting 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.
Once we've converted one type, it will always work with different unsophisticated calculation. In this case, after changing .785 from its first form back again, after 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 theorems become easier to digest.
At the moment, we will convert pi/12 rad into degrees. Just the same as before, 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 generally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equals 15 degrees.
Let's try another common conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as appropriate, and you will end up with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you are required to convert degrees to radians?
By using the very same formula, you can do the contrary in a pinch by solving it considering radians as the unknown.
For example, if you want to transform 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 memorized the formula to find radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there you have it! These are just handful of examples of how to transform radians to degrees and vice versa. Remember the formula and see for yourself the next time you are required to make a conversion between radians and degrees.
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