Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for higher arithmetic learners to comprehend.
Initially, we are required to explain what radians are thereby you can understand how this theorem works in practice. Thereafter we’ll take it one 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 comes from the Latin word "radix," which means nostril or ray, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) unit for angles, although a degree is a more frequently used unit in arithmetic.
Simply put, radians and degrees are just two distinct units of measure utilized for measuring the exact thing: angles.
Note: a radian is not to be mixed with a radius. They are two entirely distinct concepts. A radius is the length from the middle of a circle to the edge, while a radian is a unit of measure for angles.
Association Between Radian and Degrees
There are two manners to think regarding this question. The initial way 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 say:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The second way to think about this question is to think about how many degrees exists in a radian. We know that there are 360 degrees in a whole circle, and we also understand that there are two pi radians in a whole 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 helpful relying upon which you're trying to do.
How to Convert Radians to Degrees?
Now that we've went through what radians and degrees are, let's practice how to turn them!
The Formula for Converting Radians to Degrees
Proportions are a helpful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just put in your given values to obtain your unknown values. For instance, if you wanted to convert .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To find 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 recheck our workings 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.
Since we've converted one type, it will always work with another straightforward calculation. In this scenario, after converting .785 from its original form back again, following these steps created exactly what was predicted -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's try a few examples, so these concepts become simpler to digest.
Now, we will transform pi/12 rad to degrees. Just like previously, we will put this number into the radians slot of the formula and solve 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 equivalents 15 degrees.
Let's try one more common conversion and transform 1.047 rad to degrees. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as appropriate, and you will wind up with 60 degrees! (59.988 degrees to be almost exact).
Right away, what to do if you are required to change degrees to radians?
By employing the very same formula, you can do the contrary in a pinch by solving for radians as the unknown.
For example, if you wish 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 change radians to degrees and the other way around. Keep in mind the formula and try it out for yourself the next time you have to make a transformation among radians and degrees.
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