Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for advanced arithmetic students to understand.
Initially, we are required to define what radians are thereby you can perceive 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 measurement units for angles. It is derived from the Latin word "radix," which suggests ray or nostril, and is a fundamental concept in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more frequently utilized unit in mathematics.
That being said, radians and degrees are simply two distinct units of measure employed for measuring the identical thing: angles.
Note: a radian is not to be confused with a radius. They are two completely different things. A radius is the length from the middle of a circle to the border, whereas a radian is a measuring unit for angles.
Correlation Between Radian and Degrees
We have two manners to think regarding this question. The initial method is to figure out about how many radians are present in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). Therefore, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to figure out regarding this question is to calculate how many degrees there are in a radian. We know that there are 360 degrees in a complete circle, and we also know that there are two pi radians in a full 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 helpful relying on what you're trying to do.
How to Change Radians to Degrees?
Now that we've gone through what degrees and radians are, let's practice how to turn them!
The Formula for Converting Radians to Degrees
Proportions are a beneficial tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply plug in your given values to obtain your unknown values. For instance, if you are required to turn .7854 radians to degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To find out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s verify our work by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Since we've changed one type, it will always work with another straightforward calculation. In this instance, after changing .785 from its original form back again, ensuing these steps created perfectly what was expected -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's attempt some examples, so these ideas become easier to digest.
Now, we will change pi/12 rad to degrees. Just the same as previously, we will put 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 generally do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equals 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as suitable, and you will end up with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you have to transform degrees to radians?
By using the very exact formula, you can do the converse in a pinch by solving it considering radians as the unknown.
For example, if you have 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 remember the formula to find radians, you will get the same thing:
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 conversely. Remember the equation 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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