Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for progressive arithmetic students to grasp.
Initially, we are required to explain what radians are so that you can perceive how this theorem is used in practice. Thereafter we’ll take it one step further by exhibiting some examples of converting from radians to degrees with ease!
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a critical idea in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more generally used unit in math.
That being said, radians and degrees are merely two different units of measure employed for measuring the identical thing: angles.
Note: a radian is not to be mistaken with a radius. They are two absolety distinct things. A radius is the distance from the middle of a circle to the perimeter, though a radian is a unit of measure for angles.
Correlation Between Radian and Degrees
There are two ways to think regarding this question. The first 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 (exactly). Hence, we can state:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The next way to think regarding this question is to think about how many degrees exists in a radian. We know that there are 360 degrees in a full circle, and we also know 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 useful depending on what you're trying to do.
How to Go From Radians to Degrees?
Now that we've covered what radians and degrees are, let's practice how to turn 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
Just put in your known values to obtain your unknown values. For example, if you are required to turn .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula can be implemented both ways. Let’s verify our workings by converting 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.
Once we've changed one type, it will always work with another unsophisticated calculation. In this scenario, after converting .785 from its first form back again, after these steps produced exactly what was anticipated -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's attempt a handful of examples, so these ideas become easier to digest.
At the moment, we will change pi/12 rad to degrees. Much like before, 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 normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equals 15 degrees.
Let's try one more general 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 appropriate, and you will wind up with 60 degrees! (59.988 degrees to be almost exact).
Now, what to do if you are required to transform degrees to radians?
By utilizing the very same formula, you can do the converse in a pinch by solving it considering radians as the unknown.
For example, if you want to transform 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 remember the formula 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 handful of examples of how to transform radians to degrees and the other way around. Keep in mind the formula and try solving for yourself the next time you need to make a conversion between radians and degrees.
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