Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for progressive arithmetic students to grasp.
Initially, we are required to explain what radians are thereby you can perceive how this formula is used in practice. Then we’ll take a further step by exhibiting a few examples of converting from radians to degrees quickly!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which means ray or nostril, and is a critical theory in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, while a degree is a more frequently used unit in mathematics.
That being said, radians and degrees are merely two distinct units of measure used for measuring the identical thing: angles.
Note: a radian is not to be mistaken with a radius. They are two entirely different things. A radius is the distance from the center of a circle to the perimeter, whereas a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
We have two manners to think regarding this question. The initial method is to contemplate 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 think about this question is to think about how many degrees are present in a radian. We understand that there are 360 degrees in a whole circle, and we also know 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 Change Radians to Degrees?
Since we've went through what radians and degrees are, let's practice how to change them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease put in your known values to get your unknown values. For example, if you wanted to turn .7854 radians to degrees, your proportion will be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula can be implemented both ways. Let’s double-check our work by changing 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find out the value of y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Now that we've transformed one type, it will always work with another simple calculation. In this instance, after converting .785 from its original form back again, after these steps made 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 try a few examples, so these ideas become easier to digest.
At the moment, we will transform pi/12 rad into degrees. Much like before, we will put this number into 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 would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have it! pi/12 radians equivalents 15 degrees.
Let's try some more general conversion and transform 1.047 rad to degrees. Once again, use the formula to get started:
Degrees = (180 * 1.047) / π
One more time, you multiply and divide as suitable, and you will wind up with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you want to transform degrees to radians?
By using the very same formula, you can do the opposite 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 solve for the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you memorized the formula to solve for 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 a few examples of how to convert radians to degrees and conversely. Remember the equation and try it out for yourself the next time you are required to make a change from or to radians and degrees.
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