Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very essential ability for progressive math learners to grasp.
First, we need to define what radians are thereby you can perceive how this formula is used in practice. After that we’ll take it one step further by exhibiting a few examples of going 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 means ray or nostril, and is a critical idea in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, although a degree is a more commonly used unit in math.
In other words, radians and degrees are just two separate units of measure employed for measuring the identical thing: angles.
Note: a radian is not to be mixed with a radius. They are two completely distinct concepts. A radius is the length from the center of a circle to the edge, whereas a radian is a unit of measure for angles.
Relationship Between Radian and Degrees
We have two manners to think about this question. The first way is to figure out about how many radians there are in a full circle. A full circle is equivalent to 360 degrees or two pi radians (precisely). Therefore, we can state:
2π radians = 360 degrees
Or simply:
π radians = 180 degrees
The second way to figure out regarding this question is to calculate how many degrees exists in a radian. We understand that there are 360 degrees in a whole 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 notice that 1 radian is about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial depending upon which you're trying to get.
How to Convert Radians to Degrees?
Since we've covered what degrees and radians are, let's find out how to change them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial 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 wished 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 verify 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.
Now that 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, ensuing these steps produced precisely what was anticipated -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's attempt some examples, so these theorems become simpler to digest.
Now, we will transform pi/12 rad into degrees. Much like previously, we will put this value 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 equals 15 degrees.
Let's try another 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 appropriate, and you will end up with 60 degrees! (59.988 degrees to be exact).
Now, what to do if you have to change degrees to radians?
By using the very exact formula, you can do the opposite in a pinch by solving for radians as the unknown.
For example, if you wish to convert 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 recollect 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 some of the examples of how to change radians to degrees and vice versa. Keep in mind the equation and see for yourself the next time you need to make a change among radians and degrees.
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