Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for progressive arithmetic students to comprehend.
Initially, we are required to define what radians are in order that you can perceive how this formula works in practice. Then we’ll take a further step by showing some examples of converting from radians to degrees easily !
What Is a Radian?
Radians are measurement units for angles. It comes from the Latin word "radix," which suggests nostril or ray, and is a fundamental theory in geometry and mathematics.
A radian is the SI (standard international) unit for angles, even though a degree is a more generally utilized unit in mathematics.
That being said, radians and degrees are simply two distinct units of measure utilized for measuring the same thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely separate concepts. A radius is the length from the middle of a circle to the edge, though a radian is a unit of measure for angles.
Association Between Radian and Degrees
There are two ways to think about this question. The initial 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 (exactly). Hence, we can say:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The second way to figure out about this question is to calculate how many degrees are present 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 complete circle.
If we divide each side by π radians, we’ll get that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial depending upon which you're trying to get.
How to Change Radians to Degrees?
Since we've went through what radians and degrees are, let's find out how to change them!
The Formula for Giong From Radians to Degrees
Proportions are a helpful tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply put in your given values to obtain your unknown values. For instance, if you wished to convert .7854 radians to degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To solve for z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula can be implemented both ways. Let’s recheck our work by converting 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 changed one type, it will always work with different straightforward calculation. In this scenario, afterwards converting .785 from its original form back again, ensuing these steps created precisely what was expected -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 concepts become easier to digest.
At the moment, we will convert pi/12 rad to degrees. Just like previously, we will place this value 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 usually do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equivalents 15 degrees.
Let's try some more common conversion and transform 1.047 rad to degrees. Once again, use 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 are required to change degrees to radians?
By employing the very same formula, you can do the contrary in a pinch by work out with radians as the unknown.
For example, if you have to transform 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 remember the equation 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 conversely. Remember the equation and try it out for yourself the next time you need to make a conversion between radians and degrees.
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