Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for advanced arithmetic learners to understand.
Initially, we are required to define what radians are in order that you can perceive how this theorem is used in practice. Thereafter we’ll take it one step further by exhibiting a few examples of changing from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a fundamental idea in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, while a degree is a more generally utilized unit in mathematics.
Simply put, radians and degrees are simply two distinct units of measure used for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two completely distinct things. A radius is the distance from the middle of a circle to the edge, whereas a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
There are two ways to go about regarding this question. The initial way is to contemplate about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (precisely). Therefore, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to think regarding this question is to calculate how many degrees there are in a radian. We know that there are 360 degrees in a whole circle, and we also recognize that there are two pi radians in a whole circle.
If we divide each side by π radians, we’ll see 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 Change Radians to Degrees?
Since we've gone through what degrees and radians are, let's find out how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a useful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to derive your unknown values. For instance, if you wanted to convert .7854 radians to degrees, your proportion will 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 works both ways. Let’s verify 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.
Now that we've changed one type, it will always work out with another unsophisticated calculation. In this instance, after converting .785 from its original form back again, following these steps created exactly what was predicted -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's attempt a handful of examples, so these concepts become simpler to digest.
Now, we will convert pi/12 rad to degrees. Just the same as previously, we will put this number in 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 answer! pi/12 radians equals 15 degrees.
Let's try another general conversion and transform 1.047 rad to degrees. Yet 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 precise).
Now, what happens if you want to convert degrees to radians?
By utilizing the very exact formula, you can do the opposite in a pinch by solving for radians as the unknown.
For example, if you wish to convert 60 degrees to radians, plug 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 a few examples of how to change radians to degrees and conversely. Bear in mind the formula and try solving for yourself the next time you are required to make a change from or to radians and degrees.
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