Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important skill for higher math students to understand.
Initially, we are required to define what radians are thereby you can see how this theorem works in practice. Then we’ll take a further step by looking at some examples of going from radians to degrees easily !
What Is a Radian?
Radians are units of measurement for angles. It is originated from the Latin word "radix," which suggests nostril or ray, and is a critical theory in mathematics and geometry.
A radian is the SI (standard international) measuring unit for angles, although a degree is a more generally used unit in math.
Simply put, radians and degrees are simply two distinct units of measure utilized for measuring the identical thing: angles.
Note: a radian is not to be confused with a radius. They are two absolety separate 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
There are two manners to go about 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 (exactly). Therefore, we can state:
2π radians = 360 degrees
Or easily:
π radians = 180 degrees
The second way to think regarding this question is to calculate how many degrees are present in a radian. We know that there are 360 degrees in a complete circle, and we also understand 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 beneficial relying on what you're trying to get.
How to Go From Radians to Degrees?
Now that we've went through 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 converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Just plug in your given values to obtain your unknown values. For instance, if you wanted 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 with .7854 and divide by 3.14 (pi): 45 degrees.
This formula implied both ways. Let’s double-check our operation 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.
Since we've changed one type, it will always work out with another straightforward calculation. In this scenario, afterwards changing .785 from its original form back again, ensuing these steps made precisely what was predicted -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's try some examples, so these ideas become simpler to digest.
At the moment, we will change pi/12 rad to degrees. Just the same as previously, we will put this value into the radians slot of the formula and solve it like this:
Degrees = (180 * (π/12)) / π
Now, let divide and multiply as you normally would:
Degrees = (180 * (π/12)) / π = 15 degrees.
There you have the answer! pi/12 radians equals 15 degrees.
Let's try some more general conversion and transform 1.047 rad to degrees. Yet again, utilize the formula to get started:
Degrees = (180 * 1.047) / π
Yet again, you multiply and divide as appropriate, and you will wind up with 60 degrees! (59.988 degrees to be almost exact).
Now, what to do if you have to change degrees to radians?
By using the very exact formula, you can do the converse in a pinch by solving it considering radians as the unknown.
For example, if you want to change 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 memorized the equation to find 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 a few examples of how to change radians to degrees and the other way around. Keep in mind the formula and see for yourself the next time you are required to make a change among radians and degrees.
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