Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for higher arithmetic learners to understand.
First, we need to define what radians are in order that you can see how this formula works in practice. Then we’ll take this a step further by showing a few examples of changing from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which suggests ray or nostril, and is a fundamental concept in mathematics and geometry.
A radian is the SI (standard international) unit for angles, while a degree is a more commonly utilized unit in math.
In other words, radians and degrees are simply two distinct 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 concepts. A radius is the distance from the center of a circle to the perimeter, whereas a radian is a unit of measure for angles.
Correlation Between Radian and Degrees
We have two manners to go about regarding this question. The first method 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 (exactly). So, we can state:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to think about this question is to consider how many degrees exists in a radian. We understand that there are 360 degrees in a complete circle, and we also understand that there are two pi radians in a full circle.
If we divide each side by π radians, we’ll see that 1 radian is approximately 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 do.
How to Change Radians to Degrees?
Now that we've covered what radians and degrees are, let's practice how to convert 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
Simply plug in your known values to derive your unknown values. For example, if you are required to turn .7854 radians to degrees, your proportion would 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 works both ways. Let’s recheck our operation by changing 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.
Since we've converted one type, it will always work with different unsophisticated calculation. In this scenario, after converting .785 from its original form back again, after these steps made perfectly 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 try some examples, so these ideas become easier to digest.
Now, we will transform pi/12 rad into degrees. Just like before, we will plug this number 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 would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equals 15 degrees.
Let's try another general conversion and transform 1.047 rad to degrees. Yet again, use the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as suitable, and you will end up with 60 degrees! (59.988 degrees to be precise).
Right away, what happens if you want to change degrees to radians?
By utilizing the very exact formula, you can do the converse in a pinch by solving for radians as the unknown.
For example, if you want to convert 60 degrees to radians, put in the knowns and work out with 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 change radians to degrees and the other way around. Bear in mind the formula and try solving for yourself the next time you have to make a conversion from or to radians and degrees.
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