Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important ability for progressive arithmetic students to grasp.
Initially, we are required to specify what radians are thereby you can see how this theorem works in practice. Then we’ll take a further step by showing some examples of changing from radians to degrees quickly!
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which implies nostril or ray, and is a essential concept in geometry and mathematics.
A radian is the SI (standard international) unit of measurement for angles, although a degree is a more commonly used unit in arithmetic.
In other words, radians and degrees are just two separate units of measure used for measuring the identical thing: angles.
Note: a radian is not to be mixed with a radius. They are two absolety separate things. A radius is the distance from the middle of a circle to the edge, though a radian is a unit of measure for angles.
Association Between Radian and Degrees
There are two ways to think regarding this question. The first way is to figure out about how many radians are present in a full circle. A full circle is equals to 360 degrees or two pi radians (precisely). Therefore, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The next way to figure out about this question is to consider how many degrees are present in a radian. We all know that there are 360 degrees in a whole circle, and we also recognize that there are two pi radians in a complete circle.
If we divide each side by π radians, we’ll notice that 1 radian is approximately 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 do.
How to Go From Radians to Degrees?
Since we've gone through what radians and degrees are, let's learn how to turn them!
The Formula for Changing Radians to Degrees
Proportions are a beneficial tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your given values to get your unknown values. For instance, if you are required to convert .7854 radians to degrees, your proportion will 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 implied both ways. Let’s recheck our workings by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 by 3.14 (pi) and divide by 180: .785 radians.
Since we've changed one type, it will always work with different simple calculation. In this instance, after converting .785 from its original form back again, after these steps made precisely what was expected -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 go through a few examples, so these ideas become simpler to digest.
At the moment, we will change pi/12 rad into degrees. Much like previously, we will plug 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 the answer! pi/12 radians equivalents 15 degrees.
Let's try some more common 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 suitable, and you will find yourself with 60 degrees! (59.988 degrees to be precise).
Now, what happens if you want to transform degrees to radians?
By utilizing the very exact formula, you can do the converse in a pinch by work out with radians as the unknown.
For example, if you have to convert 60 degrees to radians, put 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 same thing:
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 transform radians to degrees and vice versa. Bear in mind the formula and try it out for yourself the next time you have to make a conversion among radians and degrees.
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