Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for progressive arithmetic students to understand.
First, we need to define what radians are thereby you can see how this formula is used in practice. After that we’ll take this a step further by showing some examples of changing from radians to degrees easily !
What Is a Radian?
Radians are measurement units for angles. It is originated from the Latin word "radix," which implies ray or nostril, and is a fundamental theory in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, even though a degree is a more generally utilized unit in math.
In other words, radians and degrees are simply 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 completely distinct things. A radius is the length from the center of a circle to the perimeter, while a radian is a unit of measure for angles.
Association Between Radian and Degrees
We have two manners to go about regarding this question. The first 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). Hence, we can say:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to figure out regarding this question is to consider how many degrees there are 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 whole 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 useful depending on what you're trying to do.
How to Go From Radians to Degrees?
Now that we've went through what degrees and radians are, let's find out how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a useful tool for changing a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to obtain your unknown values. For instance, if you wished to convert .7854 radians to 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 works both ways. Let’s recheck our operation by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To solve for y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Once we've converted one type, it will always work out with different straightforward calculation. In this case, after converting .785 from its first form back again, after these steps produced precisely what was expected -45°.
The formulas work out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Going From Radians to Degrees
Let's try some examples, so these ideas become easier to digest.
Now, we will change pi/12 rad to degrees. Much like before, we will put this value in the radians slot of the formula and solve it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you generally 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 appropriate, and you will find yourself with 60 degrees! (59.988 degrees to be exact).
Right away, what to do if you are required to transform degrees to radians?
By employing the very exact formula, you can do the contrary in a pinch by work out with radians as the unknown.
For example, if you want 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 same thing:
Radians = (π * z degrees) / 180
Radians = (π * 60 degrees) / 180
And there it is! These are just some of the examples of how to transform radians to degrees and vice versa. Remember the equation and see for yourself the next time you are required to make a change between radians and degrees.
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