Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for advanced math students to comprehend.
First, we need to explain what radians are thereby you can see how this formula is used in practice. Then we’ll take it one step further by looking at a few examples of changing from radians to degrees with ease!
What Is a Radian?
Radians are units of measurement for angles. It comes from the Latin word "radix," which implies nostril or ray, and is a fundamental concept in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, even though a degree is a more commonly used unit in arithmetic.
That being said, radians and degrees are simply two different units of measure utilized 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 middle of a circle to the edge, while a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
There are two ways to go about about this question. The first way is to think about how many radians are present in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). So, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to think regarding this question is to calculate how many degrees are present in a radian. We understand that there are 360 degrees in a full circle, and we also recognize that there are two pi radians in a complete 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 helpful relying upon which you're trying to get.
How to Go From 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 useful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known 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 solve for z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s recheck our work by reverting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Now that we've transformed one type, it will always work out with another unsophisticated calculation. In this case, afterwards converting .785 from its original form back again, after these steps created perfectly what was predicted -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's attempt a few examples, so these concepts become easier to digest.
Now, we will convert pi/12 rad to degrees. Just the same as before, we will place this number 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 do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equivalents 15 degrees.
Let's try another 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 happens if you are required to transform degrees to radians?
By employing the very same formula, you can do the contrary in a pinch by solving for radians as the unknown.
For example, if you want to change 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 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 some of the examples of how to change radians to degrees and conversely. Bear in mind the equation and try it out for yourself the next time you need to make a transformation from or to radians and degrees.
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