Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for advanced arithmetic learners to understand.
First, we are required to explain what radians are in order that you can perceive how this formula is used in practice. After that we’ll take this a step further by showing a few examples of changing from radians to degrees easily !
What Is a Radian?
Radians are measurement units for angles. It comes from the Latin word "radix," which suggests nostril or ray, and is a critical theory in geometry and mathematics.
A radian is the SI (standard international) measuring unit for angles, although a degree is a more commonly utilized unit in math.
In other words, radians and degrees are just two distinct units of measure employed for measuring the same thing: angles.
Note: a radian is not to be mixed with a radius. They are two completely distinct things. A radius is the distance from the center of a circle to the perimeter, though a radian is a unit of measure for angles.
Correlation Between Radian and Degrees
We have two ways to think about this question. The initial method is to contemplate about how many radians exists in a full circle. A full circle is equals to 360 degrees or two pi radians (exactly). Therefore, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to think regarding this question is to think about how many degrees are present in a radian. We know 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 about 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are helpful relying on what you're trying to do.
How to Change Radians to Degrees?
Now that we've went through what degrees and radians are, let's practice how to turn 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 plug in your known values to derive your unknown values. For example, if you wanted to convert .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 implied both ways. Let’s double-check our workings by converting 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.
Once we've changed one type, it will always work out with another unsophisticated calculation. In this case, afterwards changing .785 from its original form back again, after these steps produced precisely what was predicted -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 go through some examples, so these theorems become simpler to digest.
At the moment, we will convert pi/12 rad into degrees. Just the same as before, we will plug this value in 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 do:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the result! pi/12 radians equals 15 degrees.
Let's try one more general conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Once again, you multiply and divide as fitting, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Now, what happens if you want to transform degrees to radians?
By employing the very exact formula, you can do the opposite in a pinch by solving for radians as the unknown.
For example, if you have to change 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 remember the equation to solve for radians, you will get the exact result:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just some of the examples of how to change radians to degrees and conversely. Keep in mind the formula and try solving for yourself the next time you have to make a change from or to radians and degrees.
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