Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for progressive math learners to understand.
Initially, we are required to define what radians are in order that you can perceive how this theorem works in practice. Then we’ll take this a step further by looking at a few examples of going from radians to degrees with ease!
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a fundamental idea 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 mathematics.
In other words, radians and degrees are just two different units of measure used for measuring the exact thing: angles.
Note: a radian is not to be confused with a radius. They are two entirely different things. A radius is the length from the center of a circle to the edge, though a radian is a measuring unit for angles.
Association Between Radian and Degrees
We have two manners to think about this question. The first method is to contemplate about how many radians are present in a full circle. A full circle is equal to 360 degrees or two pi radians (exactly). Therefore, we can state:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The second way to think about this question is to consider how many degrees are present in a radian. We know that there are 360 degrees in a complete circle, and we also understand that there are two pi radians in a full circle.
If we divide each side by π radians, we’ll get that 1 radian is approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial relying upon which you're trying to get.
How to Convert Radians to Degrees?
Now that we've went through what radians and degrees are, let's learn how to change them!
The Formula for Converting Radians to Degrees
Proportions are a useful tool for converting a radian value into degrees.
π radiansx radians = 180 degreesy degrees
Simply put in your given values to derive your unknown values. For example, if you wished to change .7854 radians into degrees, your proportion would 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 converting 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.
Once we've converted one type, it will always work with different straightforward calculation. In this case, after converting .785 from its first form back again, ensuing these steps produced precisely what was expected -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's attempt some examples, so these concepts become easier to digest.
At the moment, we will change pi/12 rad to degrees. Much like previously, we will plug 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 normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! 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
Yet 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 change degrees to radians?
By employing the very same formula, you can do the converse in a pinch by work out with radians as the unknown.
For example, if you wish to convert 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 recollect the equation to find radians, you will get the same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just a few examples of how to change radians to degrees and the other way around. Bear in mind the equation and see for yourself the next time you have to make a transformation from or to radians and degrees.
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