Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for advanced arithmetic learners to understand.
First, we are required to define what radians are in order that you can perceive how this theorem is used in practice. After that we’ll take this a step further by showing some examples of going from radians to degrees quickly!
What Is a Radian?
Radians are units of measurement for angles. It comes from the Latin word "radix," which suggests ray or nostril, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, while a degree is a more frequently used unit in arithmetic.
Simply put, radians and degrees are just two separate units of measure used for measuring the identical thing: angles.
Note: a radian is not to be mistaken with a radius. They are two completely distinct things. A radius is the length from the center of a circle to the perimeter, whereas a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two ways to go about regarding this question. The initial method is to figure out about how many radians exists 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 simply:
π radians = 180 degrees
The second way to think about this question is to calculate how many degrees are present in a radian. We all 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 see that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful depending 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 Giong From Radians to Degrees
Proportions are a helpful tool for changing a radian value into degrees.
π radiansx radians = 180 degreesy degrees
With ease put in your known values to obtain your unknown values. For instance, if you wished to change .7854 radians to degrees, your proportion will 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 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.
Now that we've converted one type, it will always work with different straightforward calculation. In this instance, afterwards changing .785 from its first form back again, following these steps produced precisely 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 go through some examples, so these theorems become easier to digest.
Now, we will convert pi/12 rad into degrees. Much like previously, we will place 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 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 precise).
Right away, what happens if you have to convert degrees to radians?
By employing the very exact formula, you can do the opposite in a pinch by work out with radians as the unknown.
For example, if you want to convert 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 it is! These are just a few examples of how to transform radians to degrees and vice versa. Remember the formula and try solving for yourself the next time you need to make a change among radians and degrees.
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