Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very crucial skill for progressive arithmetic learners to grasp.
Initially, we are required to specify what radians are so that you can see how this theorem is used in practice. Then we’ll take it one step further by showing some examples of changing from radians to degrees with ease!
What Is a Radian?
Radians are measurement units for angles. It comes 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) measuring unit for angles, although a degree is a more generally used unit in arithmetic.
That being said, radians and degrees are merely two distinct units of measure used for measuring the same thing: angles.
Note: a radian is not to be confused with a radius. They are two completely separate concepts. A radius is the length from the center of a circle to the border, whereas a radian is a measuring unit for angles.
Relationship Between Radian and Degrees
We have two ways to think regarding this question. The initial way is to think about how many radians are present in a full circle. A full circle is equivalent to 360 degrees or two pi radians (exactly). Hence, we can state:
2π radians = 360 degrees
Or simplified:
π radians = 180 degrees
The second way to think regarding this question is to think about how many degrees exists in a radian. We know that there are 360 degrees in a complete 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 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 Change Radians to Degrees?
Now that we've covered what radians and degrees are, let's find out how to change them!
The Formula for Converting Radians to Degrees
Proportions are a beneficial tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
Simply put in your given values to obtain your unknown values. For example, if you wanted to convert .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To solve for z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula works both ways. Let’s double-check our operation by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To work out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Since we've transformed one type, it will always work with another simple calculation. In this case, afterwards converting .785 from its first form back again, ensuing these steps made exactly what was anticipated -45°.
The formulas plays out like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Converting Radians to Degrees
Let's go through a handful of examples, so these concepts become easier to digest.
Now, we will convert pi/12 rad into degrees. Just like before, we will place this number into the radians slot of the formula and calculate 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. One more time, use the formula to get started:
Degrees = (180 * 1.047) / π
Once again, you multiply and divide as suitable, and you will wind up with 60 degrees! (59.988 degrees to be precise).
Now, what to do if you want to transform degrees to radians?
By utilizing the very same 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, put in the knowns and work out with the unknowns:
60 degrees = (180 * z radians) / π
(60 * π)/180 = 1.047 radians
If you remember the formula to find 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 convert radians to degrees and conversely. Remember the formula and try it out for yourself the next time you are required to make a transformation between radians and degrees.
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