Radians to Degrees - Conversion, Formula, Examples
Radians and degrees conversion is a very important skill for higher math students to grasp.
First, we are required to specify what radians are thereby you can perceive how this theorem works in practice. Then we’ll take it one step further by looking at a few examples of going from radians to degrees with ease!
What Is a Radian?
Radians are measurement units for angles. It is derived from the Latin word "radix," which means nostril or ray, and is a critical theory in mathematics and geometry.
A radian is the SI (standard international) unit of measurement for angles, even though a degree is a more commonly utilized unit in mathematics.
Simply put, radians and degrees are simply two different units of measure utilized 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 distance from the middle of a circle to the edge, though a radian is a unit of measure for angles.
Correlation Between Radian and Degrees
We have two ways to think regarding this question. The first method is to figure out 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 simply:
π radians = 180 degrees
The next way to think regarding this question is to consider how many degrees there are in a radian. We understand that there are 360 degrees in a full 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 approximately 57.296 degrees.
π radiansπ radians = 180 degreesπ radians = 57.296 degrees
Both of these conversion factors are beneficial relying upon which you're trying to get.
How to Go From Radians to Degrees?
Now that we've covered what radians and degrees are, let's practice how to convert them!
The Formula for Converting Radians to Degrees
Proportions are a helpful tool for converting a radian value to degrees.
π radiansx radians = 180 degreesy degrees
With ease plug in your known values to derive your unknown values. For instance, if you are required to convert .7854 radians into degrees, your proportion would be:
π radians.7854 radians = 180 degreesz degrees
To work out the value of z, multiply 180 by .7854 and divide by 3.14 (pi): 45 degrees.
This formula can be implemented both ways. Let’s recheck our operation by converting 45 degrees back to radians.
π radiansy radians = 180 degrees45 degrees
To find out the value of y, multiply 45 with 3.14 (pi) and divide by 180: .785 radians.
Now that we've changed one type, it will always work with different straightforward calculation. In this instance, after changing .785 from its original form back again, following these steps created precisely what was anticipated -45°.
The formulas solves like this:
Degrees = (180 * z radians) / π
Radians = (π * z degrees) / 180
Examples of Changing Radians to Degrees
Let's attempt some examples, so these concepts become easier to digest.
At the moment, we will transform pi/12 rad to degrees. Just the same as before, we will plug this value in the radians slot of the formula and calculate 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 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 fitting, and you will wind up with 60 degrees! (59.988 degrees to be precise).
Now, what happens if you are required to transform degrees to radians?
By employing the very exact formula, you can do the opposite in a pinch by solving it considering radians as the unknown.
For example, if you want 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 memorized the equation to find 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 vice versa. Remember the equation and try it out for yourself the next time you have to make a change from or to radians and degrees.
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