Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial ability for higher mathematics students to grasp.
First, we are required to explain what radians are so that you can perceive how this theorem works in practice. After that we’ll take this a step further by showing some examples of converting 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 implies nostril or ray, and is a essential concept in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, although a degree is a more commonly used unit in mathematics.
That being said, radians and degrees are merely two distinct units of measure employed for measuring the exact thing: angles.
Note: a radian is not to be mixed with a radius. They are two absolety separate things. A radius is the length from the middle of a circle to the edge, while a radian is a measuring unit for angles.
Relationship Between Radian and Degrees
There are two ways to think regarding this question. The first method is to figure out about how many radians exists in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). 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 understand that there are 360 degrees in a full circle, and we also recognize 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 useful relying upon which you're trying to do.
How to Convert Radians to Degrees?
Since we've covered what degrees and radians are, let's find out how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a helpful tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your known values to derive your unknown values. For instance, if you are required to convert .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 implied both ways. Let’s double-check our operation by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Since we've transformed one type, it will always work with another straightforward calculation. In this case, after changing .785 from its first form back again, following these steps made 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 a handful of examples, so these ideas become simpler to digest.
At the moment, we will change pi/12 rad into degrees. Just like before, we will put this value in 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 it! pi/12 radians equals 15 degrees.
Let's try one more 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 fitting, and you will end up with 60 degrees! (59.988 degrees to be exact).
Now, what happens if you have to convert degrees to radians?
By employing 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 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 it is! These are just a few examples of how to convert radians to degrees and the other way around. Remember the equation and try it out for yourself the next time you have to make a change among radians and degrees.
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